The square root of a negative number results in complex solutions, it indicates that there are no real values of ω that satisfy the equation. For the given system, there is no real phase crossover frequency.
To calculate the phase crossover frequency for the
given system, we need to determine the frequency at which the phase of the open-loop transfer function becomes -180 degrees (or π radians).
The open-loop transfer function is given as G(s) = 5s(s + 4)(s + 10).
Let's find the phase crossover frequency algebraically:
Substitute s = jω into the transfer function, where j is the imaginary unit and ω is the angular frequency.
G(jω) = 5(jω)(jω + 4)(jω + 10)
Express G(jω) in polar form (magnitude and phase):
G(jω) = |G(jω)| * e^(jθ)
where |G(jω)| is the magnitude and θ is the phase.
Set the phase θ equal to -π radians (-180 degrees):
θ = -π
Solve for the frequency ω at the phase crossover:
5(jω)(jω + 4)(jω + 10) = |G(jω)| * e^(-jπ)
Simplify the left-hand side:
-5ω(ω + 4)(ω + 10) = |G(jω)| * e^(-jπ)
To solve this equation, we need to find the magnitude |G(jω)|.
|G(jω)| = |5(jω)(jω + 4)(jω + 10)|
|G(jω)| = 5|jω||jω + 4||jω + 10|
|G(jω)| = 5 * ω * sqrt(ω^2 + 4^2) * sqrt(ω^2 + 10^2)
Substitute |G(jω)| back into the equation:
-5ω(ω + 4)(ω + 10) = 5 * ω * sqrt(ω^2 + 4^2) * sqrt(ω^2 + 10^2) * e^(-jπ)
Cancel out the common factors of 5 and ω:
-(ω + 4)(ω + 10) = sqrt(ω^2 + 4^2) * sqrt(ω^2 + 10^2) * e^(-jπ)
Square both sides of the equation to eliminate the square roots:
(ω + 4)^2 (ω + 10)^2 = (ω^2 + 4^2) (ω^2 + 10^2) * e^(-2jπ)
Simplify both sides of the equation:
(ω^2 + 8ω + 16) (ω^2 + 20ω + 100) = (ω^2 + 16) (ω^2 + 100) * e^(-2jπ)
Expand and rearrange terms:
ω^4 + 28ω^3 + 200ω^2 + 640ω + 1600 = ω^4 + 116ω^2 + 1600 * e^(-2jπ)
Cancel out the common terms on both sides:
28ω^3 + 84ω^2 + 640ω = 116ω^2
Simplify the equation:
28ω^3 - 32ω^2 + 640ω = 0
Factor out ω:
ω(28ω^2 - 32ω + 640) = 0
Solve for ω:
28ω^2 - 32ω + 640 = 0
Using the quadratic formula:
ω = (-(-32) ± sqrt((-32)^2 - 4 * 28 * 640)) / (2 * 28)
ω = (32 ± sqrt(1024 - 71680)) / 56
ω = (32 ± sqrt(-70656)) / 56
Since the square root of a negative number results in complex solutions, it indicates that there are no real values of ω that satisfy the equation.
Therefore, for the given system, there is no real phase crossover frequency.
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The sample space of an experiment consists of all undergraduates at a university. Give four examples of partitions.
Sure! A partition of a sample space is a collection of subsets of the sample space that are disjoint (do not overlap) and together cover the entire sample space. Here are four examples of partitions for the sample space of all undergraduates at a university:
1. Partition by gender: This partition consists of two subsets - one containing all male undergraduates and the other containing all female undergraduates. These subsets are disjoint and together cover the entire sample space.
2. Partition by major: This partition consists of subsets for each major offered at the university, such as biology, economics, history, etc. Each undergraduate would belong to exactly one of these subsets, and they are disjoint and together cover the entire sample space.
3. Partition by year: This partition consists of subsets for each year of undergraduate study, such as freshman, sophomore, junior, and senior. Again, each undergraduate would belong to exactly one of these subsets, and they are disjoint and together cover the entire sample space.
4. Partition by residence hall: This partition consists of subsets for each residence hall on campus, such as Smith Hall, Johnson Hall, etc. Each undergraduate would belong to exactly one of these subsets, and they are disjoint and together cover the entire sample space.
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Can some help me with this !!! Is 26 points!!
determine the components of each reaction at the ball and socket joint A and the tension in each cable necessary for equilibrium of the rod
The components of the reaction force in a ball and socket joint include the horizontal and vertical reaction forces.
What is a reaction force?A reaction force is an equal but oppositely directed force which forms a pair which the applied or action force.
Tension is a type of force which is present in a string or a rope supporting a body or object.
A ball and socket jont is a type of joint in the body which is able to rotate freely about an axis.
The components of the reaction force in a ball and socket joint include the horizontal and vertical reaction forces.
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Write an assembly code to input two character and print the characters ascending from low ASCII character to high ASCII character as shown
Enter the first character H
Enter the second character B
BCDEFGH
The assembly code in 8086 is used to input two characters and print the characters in ascending order based on their ASCII values.
After that, it compares the characters' ASCII values and creates a string of characters starting with the lower ASCII character and ending with the higher ASCII character, containing both characters. The created character sequence is then printed.
To produce the desired result, the assembly code in the 8086 follows a
The code is broken down as follows:
The data section of the programme is where the variables for the input characters, the counter, and the temporary character for comparison are defined.
The first character is requested by the user in the code section, and it is then saved in the variable first_char.
The second character is then requested from the user, which is then saved in the variable second_char.
The lower and upper ASCII characters are then determined by comparing the first_char and second_char's ASCII values. In the lower_char variable, it stores the lower ASCII character, while in the higher_char variable, it stores the higher ASCII letter.
The temporary character (temp_char) is assigned to the lower ASCII character and the counter is initialised by the code.
The code outputs characters from temp_char up to the highest ASCII character (higher_char) using a loop. For each cycle, the temp_char is likewise increased in order to print the subsequent character.
The ret instruction, which hands control back to the operating system, completes the programme.
The assembly code can correctly enter two characters by following these instructions, as well as identify the bottom and upper ASCII characters and print the characters in ascending order according to their ASCII values. If the user types 'H' as the first character and 'B' as the second character in the example given, the code will print the sequence 'BCDEFGH'.
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Calculate the areas under the stress-strain curve (toughness) for the materials shown in Fig. below, (a) plot them as a
function of temperature, and describe your observations. (b) As expected, the elastic modulus of the polymer decreases as
temperature increases. Using the stress-strain curves in the figure, make a plot of the modulus of elasticity versus the
temperature. Comment on the shape of the curve.
Answer:
Explanation:
Wow
a load of 12tonnes is put along a horizontal plane by a force at 30°to and above the flat. if the coefficient of sliding friction is 0.2 find the frictional force
Answer:
20368.917N
Explanation:
Frictional force (F) is the product of the Coefficient of friction and the normal reaction.
F = μN
Coefficient of friction, μ = 0.2
Normal reaction = MgCosθ
Mass, m = 12 tonnes = 12 * 1000 = 12000 kg
N = 12000 * 9.8 * cos30
N = 101844.58
F = 0.2 * 101844.58
F = 20368.917N
what is a computer device
what's better than a trophy truck and an ultra 4
Answer:
A ultra 4. that would be amazing to have that.
Answer:
I have know idea
Explanation:
In a four-stroke engine, the piston rises in the cylinder, which triggers the _______ stroke.
intake
compression
exhaust
power
Answer: It is power stroke
how to mark someone as brainliest on PC?
Answer:
i think its the same thing as laptop
u just press the crown button below answer if two people answer
Explanation:
Answer:
Just press the crown that will appear when two people answer.
Explanation:
PLEASE HELP ASAP!!! Thanks
the tubes inner surface area is 50 ft2. after beingused in the field for several months, the exchanger heats 100 gal/min of 70 f water to 122 f.a. what is the fouling factor?
The fouling factor of the tube is 0.0097 (min × ft2 × °F)/BTU.
To calculate the fouling factor, we first need to determine the overall heat transfer coefficient (U). We can use the following equation:
Q = U × A × LMTD
where Q is the heat transferred, A is the inner surface area of the tube, LMTD is the logarithmic mean temperature difference, and U is the overall heat transfer coefficient.
We know that the inner surface area of the tube is 50 ft2, and we can assume that the length of the tube (L) is 1 ft for simplicity. The LMTD can be calculated using the following equation:
LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
where ΔT1 is the temperature difference between the hot and cold fluids at the inlet, and ΔT2 is the temperature difference between the hot and cold fluids at the outlet. In this case, ΔT1 = 122 - 70 = 52°F and ΔT2 = 122 - 70 = 52°F.
Plugging in the values, we get:
Q = U × 50 × 1 × (52 / ln(52/52)) = U × 50
We also know that the flow rate of the cold fluid (water) is 100 gal/min, which is equivalent to 12.5 ft3/min. Using the specific heat of water (1 BTU/lb°F), we can calculate the heat transferred as:
Q = m × cp × ΔT = 12.5 × 8.34 × (122 - 70) = 5205 BTU/min
Equating the two expressions for Q, we get:
U × 50 = 5205
Solving for U, we get:
U = 104.1 BTU/(min × ft2 × °F)
Now we can calculate the fouling factor (Rf) using the following equation:
Rf = 1 / U - 1 / Ui
where Ui is the clean inner surface heat transfer coefficient, which can be estimated based on the properties of the fluids and the tube geometry. For a typical shell-and-tube heat exchanger, Ui is usually in the range of 200-400 BTU/(min × ft² × °F).
Assuming Ui = 300 BTU/(min × ft² × °F), we get:
Rf = 1 / 104.1 - 1 / 300 = 0.0097 (min × ft² × °F)/BTU
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Why are Airplanes fast enough to travel thru the air
Answer:
Airplanes have a small little jet on the back allowing them to get in the air but they have these big engines on the side allowing them to maintain their spot in the air
Explanation:
What does efficiency measure?
Answer:
Efficiency is defined as any performance that uses the fewest number of inputs to produce the greatest number of outputs. Simply put, you're efficient if you get more out of less.
Explanation:
Water is pumped from a lake to a storage tank 18 m above at a rate of 70 L/s while consuming 20.4 kW of electric power. Disregard any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump-motor unit (5-point), and (b) the pressure difference between the inlet and the exit of the pump (5-point).
Most organizations use a(n) ____ form to propose and document a maintenance change.A) team request
B) user request
C) change request
D) maintenance report
If an athlete can row at a rate of 50 m/min, how many days would it take to cross the Atlantic (≈3000 mi)?
The kinematics we can find the time to cross the Atlantic is 67 days.
The kinematics studies the movement of the body making relationships between the position, the speed and the acceleration of the same.
The average velocity is defined as the relation between the displacement between the time of the interval
v = \(\frac{\Delta x}{t}\)
Δt = \(\frac{\Delta x}{v}\)
Where v is the velocity, x the displacement t time
In this case they indicate the displacement is Δx = 3000 mi and the speed is v = 50 m / min
The system of units allow data to be exchanged with precision and safety, for this there is currently the international system of measurements (SI), where the unit of length is the meter and the unit of time is the second, let's reduce the magnitudes given to these units.
Δx = 3000 mi ( ) = 4.828 10⁶ m
v = 50 m / min ( ) = 0.833 m / s
Now we can calculate the time to cross the Atlantic
Δt = 4.828 10⁶ / 0.833
Δt = 5.796 10⁶ s
Let's reduce to days
Δt = 5.796 10⁶ s ( ) ( )
Δt = 67 days
In conclusion using kinematics we can find the result of the time to cross the Atlantic is 67 days.
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đạo hàm hàm boole là gì
Answer:
đạo hàm hàm boole là gì
Explanation:
Định nghĩa: Ký hiệu B = {0, 1} và Bn = {(x1, x2, …, xn) | xiB, 1≤ i ≤ n}, ở đây
B và Bn là các đại số Boole (xem 2) và 3) của Thí dụ 1). Biến x được gọi là một biến Boole nếu nó nhận các giá trị chỉ từ B. Một hàm từ Bn vào B được gọi là một hàm Boole (hay hàm đại số lôgic) bậc n.
Các hàm Boole cũng có thể được biểu diễn bằng cách dùng các biểu thức được
tạo bởi các biến và các phép toán Boole (xem Bảng 1 trong Thí dụ 1). Các biểu thức
Boole với các biến x1, x2, …, xn được định nghĩa bằng đệ quy như sau:
- 0, 1, x1, x2, …, xn là các biểu thức Boole.
- Nếu P và Q là các biểu thức Boole thì P, PQ và P+Q cũng là các biểu thức Boole.
Mỗi một biểu thức Boole biểu diễn một hàm Boole. Các giá trị của hàm này nhận
được bằng cách thay 0 và 1 cho các biến trong biểu thức đó.
Hai hàm n biến F và G được gọi là bằng nhau nếu F(a1, a2, …, an)=G(a1, a2, …,an)
với mọi a1, a2, …, anB. Hai biểu thức Boole khác nhau biểu diễn cùng một hàm Boole
được gọi là tương đương. Phần bù của hàm Boole F là hàm F với F (x1, x2, …, xn) =
),...,,( 1 2 nxxxF . Giả sử F và G là các hàm Boole bậc n. Tổng Boole F+G và tích Boole
FG được định nghĩa bởi:
(F+G)(x1, x2, …, xn) = F(x1, x2, …, xn)+G(x1, x2, …, xn),
(FG)(x1, x2, …, xn) = F(x1, x2, …, xn)G(x1, x2, …, xn).
parallel circuits???
PLEASE GIVE BRAINLIST
A parallel circuit has two or more paths for current to flow through. Voltage is the same across each component of the parallel circuit. The sum of the currents through each path is equal to the total current that flows from the source.
HOPE THIS HELPED
a caisson is a watertight enclosure that can be pumped dry so that construction activities, such as the construction of piers can take place. _______
A caisson is a watertight enclosure that can be pumped dry so that construction activities, such as the construction of piers can take place. A caisson is a watertight structure or chamber, usually made of wood, metal, or concrete, that is sunk to the bed of a river, lake, or ocean to provide a foundation or support for a bridge, building, or other structure.
A caisson is constructed onshore and then floated to the location where it is to be sunk into the water. Once in place, water is pumped out of the caisson, and construction workers enter the dry chamber to begin work on the foundation or support structure. The use of caissons has been an important development in the construction of bridges and other structures in areas with deep water or unstable soils.
A foundation called a caisson is used in construction on soft or deep water. It involves filling a series of large, watertight cylinders with concrete and sinking them into the ground. The base serves as a solid foundation for any subsequent structures. The construction of large structures like bridges, docks, and caissons is common.
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Help this is very hard and I don't get it
Answer:
yes it is very hard you should find a reccomended doctor to aid in your situation. But in the meantime how about you give me that lil brainliest thingy :p
What is a reflected ceiling plan?
An architectural design that depicts visible objects that are positioned on a room or space's ceiling is known as a Reflected Ceiling Plan (or RCP). A RCP may consist of; heights of ceilings. Materials for ceilings, such as set plaster or ceiling tiles.
Why is it crucial to have a reflecting ceiling plan?A mirrored ceiling plan is a crucial component of any project. It is equally significant to other drawings. It also guarantees that every line in your floor plan is straight. Above all, it aids vendors by letting them know how and where specific fixtures will be set up.
A mirrored ceiling design is it mirrored?The Floor Plan is mirrored in the Reflected Ceiling Plan, or "RCP." The RCP looks up, whereas the Floor Plan is looking down.
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A heat engine with a thermal efficiency of 25% is connected to an electric generator with an efficiency of 95%. A liquid fuel providing heat is consumed at 2.29 litres per hour. What is the power output in kW from the generator?
Heat of Combustion: 43.7 MJ/kg
Density of the fuel: 0.749 g/ml
Answer:
4.94 kW
Explanation:
The heat energy produced by the fuel in one hour is ...
(2.29 L/h)(0.749 kg/L)(43.7 MJ/kg) = 74.954677 MJ/h
Then the power output is ...
(74.954677 MJ/h)(1 h)/(3600 s) = 20.8207 kJ/s
Multiplying this heat energy by the efficiencies of the processes involved, the output power is ...
(20.8207 kW)(0.25)(0.95) = 4.94 kW
In an orthogonal cutting, a cylinder is turned to reduce the diameter with the following processing conditions Initial diameter Depth of cut Feed Rake angle Chip-tool contact length Cutting force Thrust force Spindle RPM 100 mm 2 mm 0.1 mm/rev 10° 0.5 mm 450 N 150 N 60 Calculate a) Shear and normal stresses on chip-tool interface b) Shear angle using the Lee and Shaffer's model c) Chip thickness d) Shear and normal stresses on shear plane e) Specific cutting energy f) Spindle horse power
In an orthogonal cutting, a cylinder is turned to reduce the diameter with the following processing conditions Initial The spindle horse power is 11.78 kW.
Shear and normal stresses on the chip-tool interface To determine the shear stress (τ) and normal stress (σ) on the chip-tool interface, the following formula will be used:τ = the thrust force, t is the chip-tool contact length, is the width of the chip.t = 0.5 mm w = 0.1 mm/rev * 2 mm = 0.2 mmτ = 450 N / (0.5 mm * 0.2 mm) = 45000 N/m²σ = 150 N / (0.5 mm * 0.2 mm) = 15000 N/m²Therefore, the shear stress on the chip-tool interface is 45000 N/m², and the normal stress is 15000 N/m².
Shear angle using the Lee and Shaffer's model Lee and Shaffer's model can be used to calculate the shear angle (ϕ) using the formula:ϕ = (1 / tan α_r) * [(1 + sin ψ) / (cos ψ)]whereα_r is the rake angle andψ is the clearance angle.α_r = 10°ψ = 90° - 10° = 80°ϕ = (1 / tan 10°) * [(1 + sin 80°) / cos 80°] = 18.19°Therefore, the shear angle is 18.19°.
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Shear stress on chip-tool interface = 300 MPa ;Normal stress on chip-tool interface = 52.17 MPa ; Shear angle = 5.74°Chip thickness = 0.57 mm ; Shear stress on shear plane = 263.16 MPa ; Normal stress on shear plane = 45.79 MPa ; Specific cutting energy = 113398.2 N/m ; Spindle horse power = 8.44 hp.
Given data:
Initial diameter = 100 mm
Depth of cut = 2 mm
Feed = 0.1 mm/rev
Rake angle = 10°
Chip-tool contact length = 0.5 mm
Cutting force = 450 N
Thrust force = 150 N
Spindle RPM = 60
Formula used:
Shear force = Cutting force - Thrust force
Chisel angle = Tan-1(1/ Tan Φ - Tan Φ / Tan λ)
Shear angle = Tan-1(Tan Φ / (Cos λ - Sin Φ Sin λ))
Chip thickness = Feed / Sin λa)
Shear and normal stresses on chip-tool interface
Chip-tool contact length, l = 0.5 mm
Shear force, Fs = Cutting force - Thrust force= 450 - 150= 300 N
Area of contact, Ac = t × l= 2 × 0.5= 1 mm2
Shear stress, τ = Fs / Ac= 300 / 1= 300 MPa
Normal force, Fn = Fs Tan λ= 300 × Tan 10°= 52.17 N
Normal stress, σ = Fn / Ac= 52.17 / 1= 52.17 MPab)
Shear angle using the Lee and Shaffer's model
Here, λ = 10°
Chisel angle, Φ = Tan-1(1 / Tan λ)= Tan-1(1 / Tan 10°)= 5.71°
Shear angle, α = Tan-1(Tan Φ / (Cos λ - Sin Φ Sin λ))= Tan-1(Tan 5.71° / (Cos 10° - Sin 5.71° Sin 10°))= Tan-1(0.1)= 5.74°c) Chip thicknessHere, λ = 10°Feed, t = 0.1 mm
Chip thickness, h = t / Sin λ= 0.1 / Sin 10°= 0.57 mmd)
Shear and normal stresses on shear plane
Shear force, Fs = 300 N
Shear plane area, As = t × d= 2 × 0.57= 1.14 mm2
Shear stress, τ = Fs / As= 300 / 1.14= 263.16 MPa
Normal stress, σ = Fn / As= 52.17 / 1.14= 45.79 MPae)
Specific cutting energy
Cutting power, Pc = Fs × vc= Fs × πdn/1000= 300 × π × 100 × 60/1000= 5669.91 W
Specific cutting energy, E = Pc / Vt= Pc / (f × Vf)= 5669.91 / (0.1 × 0.5)= 113398.2 N/mmf)
Spindle horse power
Spindle power, Ps = Pc / η= Pc / 0.9= 5669.91 / 0.9= 6299.90 W= 6.2999 kW= 8.44 hp (1 hp = 0.7457 kW)
Therefore,
Shear stress on chip-tool interface = 300 MPa
Normal stress on chip-tool interface = 52.17 MPa
Shear angle = 5.74°Chip thickness = 0.57 mm
Shear stress on shear plane = 263.16 MPa
Normal stress on shear plane = 45.79 MPa
Specific cutting energy = 113398.2 N/m
Spindle horse power = 8.44 hp
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Cite another example of information technology companies pushing the boundaries of privacy issues; apologizing, and then pushing again once scandal dies down. As long as the controversy fades, is there anything unethical about such a strategy?
Answer:
Explanation:
Tech Social Media giant FB is one of those companies. Not long ago the ceo was brought to court to accusations that his company was selling user data. Turns out this is true and they are selling their users private data to companies all over the word. Once the news turned to something else, people focused on something new but the company still continues to sell it's users data the same as before. This is completely unethical as the information belongs to the user and they are not getting anything while the corporation is profiting.
An adult has a total of about 22.3 square feet (ft2) of skin. Use the fact that 1 m is approximately equal to 3.281 feet to convert this measurement to square meters (m2).
Explanation:
1 meter ≈ 3.281 ft.
so,
1 m² = 1m×1m ≈ 3.281 × 3.281 = 10.764961 ft²
now we have 22.3 ft² of skin.
that would be then
22.3/10.764961 = 2.071535605 ≈ 2.1 m² or even more rounded ≈ 2 m²
according to marcia, identity status involves the dimensions of exploration and
According to Marcia, identity status involves the dimensions of exploration and commitment.
In Erik Erikson's theory of psychosocial development, James Marcia expanded on the concept of identity formation and proposed four identity statuses: identity diffusion, identity foreclosure, identity moratorium, and identity achievement. Marcia believed that identity formation involves two key dimensions: exploration and commitment. Exploration refers to actively seeking out and considering different identity options, such as exploring different career paths or values. Commitment, on the other hand, involves making a personal investment in an identity choice and integrating it into one's sense of self. The interplay between exploration and commitment determines an individual's identity status and their progress toward developing a coherent and stable sense of identity.
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Anthony and Angel are making plans for Friday. Anthony wants to go bowling. Angel doesn't bowl well and prefers to go ice-skating at the mall.
Anthony wants Angel to have a good time so he agrees ice-skating will be fun for both of them. Anthony's decision to go ice-skating is an example
of
O evaluation
O arbitration
Omed ation
O compromise
Answer:
4. Compromise
Explanation:
A compromise is when the two disagreeing parties give up something to make a conclusion that both are satisfied with. In this case, Anthony wants Angel to have a good time, so he gives up his bowling.
What should you do before you start welding?
Explanation:
1. Weld only in authorized areas. Make sure the area is dry, chemical free, and well ventilated.
2. Inspect the equipment before starting to use it.
3. Keep other people away, unless they are authorized to be there and are wearing the appropriate personal protective equipment.
In beams, why is the strain energy from bending moments much bigger than the strain energy from transverse shear forces? Choose one or more of the following options.
a) The stresses due to bending moments is much more than the stresses from transverse shear.
b) The strains due to bending moments is much more than the strains from transverse shear.
c) The deformations due to bending moments is much more than the deformations from transverse shear.
Answer:
a) The stresses due to bending moments is much more than the stresses from transverse shear.
c) The deformations due to bending moments is much more than the deformations from transverse shear.
Explanation:
Strain in an object suspended is a function of the stress which the suspended body passed through. The stress which is the function of the force experienced by the body over a given area helps is straining the moment. This lead to the strain energy from bending moment being greater than the strain energy from a transverse shear force.