Derive the equation of motion and find the natural frequency of vibration of the system shown in Figure (a) below.

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Q: Using Lagrange's equation derive the equation of motion of the system given below. Gravitational…

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Q: . What is the energy stored in the spring if the spring iscompressed 0.5 m?

A: Given data mass = 40 kgspring constant = 3000 N/mCompressed length = 0.5 mWe have to find the energy…

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A: The objective of a Propellor - The propeller's job is to produce a mode of acceleration for the…

Q: (a) Define the term kinematics. (b) State why knowing the kinematics of a mechanical system is…

A: Kinematics It is the study of the motion of objects, implementing equations, graphs etc. In this…

Q: "m₁ K3 K₁ K₂N = Figura 2 m3 K5 m₂ K₂

A: For solution refer below images.

Q: The pendulum of a wall clock has a time period of 2 seconds. Thus, the 'effective length' of a…

A:

Q: a)    Find the periodic-time (T) of a simple pendulum if its natural frequency (ω_n= 54+ 21) rad/s…

A: Given- A simple pendulum 1) Natural frequency ωn= 75 rad/s The time period (T)  =2πωn==2×π75 = 0.84…

Q: QUESTION 1 Suppose the frequency of a system is measured to be 2rad/s and after the addition of…

A: Frequency of spring mass system is given as  ω=km where ω, k, and m are angular frequency, spring…

Q: The differential equation governing the vibrating system is

A:

Q: State the translational equation of motion.

A: Say a body moves in a straight line from one point to another in a given direction and if all the…

Q: Explain or discuss why a constant force on the vibrating mass has no effect on the steady state…

A: Solution:   The correct answer with necessary explanation is given below:

Q: Kea F(t), Fo 2T -Fo x(1) F Vibration model The vibration model is subjected to the force shown in…

A:

Q: (b) Explain what is wrong with the system shown in Figure Q4(b).

A: We all know that the refrigerator is a device who take a heat from low temperature and reject it to…

Q: A Pendulum that has a period of 3 seconds and that is located where the acceleration due to gravity…

A: Given data:

Q: 1. Define simple harmonic motion.

A: answer :

Q: An object is in simple harmonic motion . The angular acceleration is 5 rad/s2 . When the angular…

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Q: The frequency of rotation of the machine in rad/s is Choose... + The natural frequency of the system…

A: As per our guidelines, we are supposed to answer only first three subparts in case of multiple…

Q: The cylinder in the system given below is rolling without slip, and it is attached to the side walls…

A:

Q: 3. Determine the number of degrees of freedom necessary for the analysis of the system shown in the…

A: The displacement of mass 2m = x1 The displacement of mass m =x2 Rotation of left side mass m =θ1…

Q: Two blocks are connected by an ideal string, which passes over a pulley without slipping (see…

A: Given, Tension force T1 = 50 N Tension force T2 = 87 N Radius of pulley = R = 0.1 m Angular…

Q: Q4 (a) State the difference between PMM1 and PMM2. Give an example of a PMM1 and a PMM2. (b) Explain…

A: 4 (a) Any device that violates first law of thermodynamics is called PMM1 while device that violates…

Q: Figure Q2 shows the schematic diagram of wind turbine which used in power plant. By using the exact…

A:

Q: Tuning Fork A point on the end of a tuningfork moves in simple harmonic motion described byd = a sin…

A: Let us consider a tuning fork that moves in a simple harmonic motion described by,d=a sinωtThe…

Q: Instruction: Find the radial frequency of the system using matrix. The final answer should be…

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Q: Derive the differential equation showing kinetic and potential energy

A: Given: To determine: Derive the differential equation

Q: Assuming that mass m of the rod of the pendulum shown in Figure 3-47 is small, but not negligible,…

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Q: An input cylinder with a diameter of 30 mm is connected to an output cylinder with a diameter of 80…

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Q: Suppose the frequency of a system is measured to be 2rad/s and after the addition of another mass…

A: Solution:

Q: Figure 4 (a) shows a mechanical vibratory system. When 2 lb of force (step input) is applied to the…

A: Solution:

Q: 3ms to complete one cycle. What is its frequency in Hz?

A: We know that the time period of oscillation of a wave is defined as the time taken by any element to…

Q: Derive the stiffness matrix for the systems in this figure using the indicated generalized…

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Q: design a simple mass-spring-damper, indicate the values of the system, and provide an equation where…

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Q: QUESTION 2. A smooth rod with a length of 21 is bent as in Figure 2 and small oscillations are made…

A: To Find : The beta angle. Given :  The length of the smooth rod is l=2l. The time period of minor…

Q: The Figure shows spring-mass system. what is the natural frequencies of the system? (two answers)

A:

Q: Fill in the Blank Question: Simulations that have time derivative terms in their governing equations…

A: Given question: Simulations that have time derivative terms in their governing equations are…

Q: A particle moves with a simple harmonic motion through space. it takes 3ms to complete two cycles.…

A: A system motion can be said to be simple harmonic motion when the system oscillates about its mean…

Q: Q)(a) A spring and mass system is shown in Figure P1.8. Assume that the rotation is small so that…

A: a) Determine the frequency of vibration if mass or rod is neglected.   (b) If total mass of the rod…

Q: Two DOF system means the system has 2 masses only Ture O False O

A: two degrees of freedom requres two independent coordinates to describe the motion

Q: Ikg Suppose the frequency of a system is measured to be 2rad/s and after the addition of another…

A: The given initial frequency is Squareroot (s/m)=2 rad/s s/m=4 s=4m

Q: d of Oscillations, b) Find the direction and magnitude of os

A: given:mass m=4kgforce F=60Nstretch dl=30cm

Q: A block rests on a frictionless surface and is attached to the end of a spring.  The other end of…

A: Since all the blocks rest on a frictionless surface, there is no damping, therefore, when the…

Q: A machine is supported by a rubber pad ( considered as a spring) for isolation. The pad is…

A: Given Data Deflection is 3mm = 3×10-3m

Q: i) Show variables on the figure, ii) Determine the space scale, ks=? iii) Write vector loop closure…

A: Here are two loops…

Q: Explain what is wrong with the system shown in Figure Q4(b).

A: To find: The wrong in the system. Concept used: The process of taking heat from high temperature…

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.