Derive the differential equation and find the natural frequency. Neglect friction. (Mech. Vibration)

Q: Q6. For the system as shown where the supporting surface is frictionless and I= 0.5mr², ww 2m (1, r)…

A: Given Data I=0.5mr2 (1) Equation of motion using Lagrange equation: Now displacement of mass 2m…

Q: Find the amplitude and period of the function, and sketch its graph. y = -2 cos 37x

A: The given function is Comparing it with the standard equation The amplitude of the given function…

Q: A damped spring macs has m=l2kq, K = 12N mm. and C=O.BNs/mm. Obtain the equation the displacement of…

A: Given ,  spring constant  k =12N/mm =12000N/m. damping coefficient  c =0.3 Ns/mm = 300 Ns/m. mass ,…

Q: Q3\ Derive the equation of motion for the system shown in figure using Newton's second law and find…

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Q: For the system illustrated below, find the natural frequency.

A: Consider the free body diagram of the block, after displacing the x1 and x2 distance to the blocks.

Q: 2k FO 3k 3r k

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Q: Q3:-Find the natural frequency for the system shown (assume massless links) by using Energy Method.…

A: Given:

Q: A particle of mass 'm' is moving in a potential v(x) = -ax? + bx4 . Find the time period and…

A: Given data: The potential equation, Vx=-ax2+bx4. Calculate the conservative force.…

Q: A torsion pendulum is made using a steel wire of radius 0.25 and sphere of of diameter…

A: Given                                   Steel wire of radius, r = 0.25mm…

Q: If the stiffness of the spring is increased to 16 times and mass is reduced to 1/4th times the…

A: Let us take, Original stiffness = k1 Original mass = m1 New stiffness = k2 New mass = m2   From the…

Q: Find the amplitude and period of the function, and sketch its graph. y = cos 47x

A: Given equation: y =cos4πx The standard periodic functions are: Here, b is the real number and A is…

Q: Q.3 Find the natural frequency of vibration of weight W for small oscillations. Assume that the…

A: Draw the free-body diagram of the pulley. The force in the spring is W/2.

Q: Find the maximum velocity of a free vibration with a response of 4(d^2 x/dt^2) e5x = 0. Initial…

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

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Q: Find the natural frequency of the system for small oscillations.

A: Given: To determine: Natural frequency for small oscillation

Q: a. Derive the differential equations of motion and obtain the mass and stiffness matrices. b.…

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Q: Determine the natural frequency of the system shown beside using Motion equation

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Q: A. Obtain the differential equations and set them in the matrix form. B. find the natural…

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Q: Di D2-

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Q: Find the damping coefficient c for this system.

A: Given: m= 24 kg k= 3000 N/m no of cycles (N)=5 xNx0=110x: Amplitude To find: Damping coefficient c…

Q: 3.- Obtain the equation of motion and the circular natural frequency as a function of the parameters…

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Q: A small sports car deflects vertical suspension system under its own weight by 0.05m. The suspension…

A: Given, Deflection under self-weight = δ = 0.05 m Mass of car  = m= 1160 kg   Part (a): When system…

Q: Determine the natural frequency

A: To find the natural frequency.

Q: System is damped single degree of freedom and under a harmonic loading. There are 5 different F(t)…

A: Considering the system with a damped single degree of freedom and under a harmonic loading given in…

Q: Find the equivalent spring stiffness of vibration of the system shown in figure. If S1 = 5000 N/m,…

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Q: The oscillation system of free oscillation is was then released. a) What is the initial…

A: Since given  graph between displacement vs time is cosωtso displacement equation x=Acosωt where is…

Q: The total mass of the L-shaped rod shown in the figure is m. Find the period and frequency of the…

A: For solution  refer below images.

Q: A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal…

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

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Q: )find the foequency of motion. amplitude, pesiod f

A: Given Data: The weight attached to the spring is W = 3 N. The stretch of the spring corresponding…

Q: Question 2, Write the boundary conditions and show how you would drive the frequency equation for…

A: u(x,t)=ϕ(x)q(t)=[A1sin(ωc)x+A2cos(ωc)](B1sinωt+B2cosωt)where c=Eρso to drive frequency equation we…

Q: Q3/ A mass has (1 kg) connected to spring has a stiffens (16 N/m) move in simple harmonic motion…

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Q: Q2:- Find the natural frequency and the steady state amplitude of vibration for the system shown in…

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Q: A rotational spring-mass system is shown to the right. The slender rigid bar nas a mass of 18 kg and…

A: Springs generally deform under an applied force. This deformation is a function of nature of force.…

Q: Fo Find the natural frequency of the system shown in the figure (13) using the energy of the rod is…

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Q: Find the equivalent spring stiffness of vibration of the system shown in figure. If S1 = 5000 N/m,…

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Q: Find the Equation of motion thenatural Frequency syydeacdse for system below K2 X2 X3

A: For solution refer below images.

Q: by uency of the harmonic force coinc: and stiffness of an absorber that w quency of 10 Hz, if the…

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Q: k=250 N/mm 1. Find the natural frequency of the system for small oscillations. 12 kg 160 cm

A: Given, m = 12 kg L = 1.6 m k = 250 x 1000 N/mm

Q: Derive the equation of motion and find the natural frequency of the following system Uniform rigid…

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Q: E. Find the natural frequency of oscillation.

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Q: 1: the mass damper spring given in the figure on the side is a harmonic it's under the influence of…

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Q: aL

A: here, total mass of L section is 2kg so, mass of each members of L section is 1 kg. For solution…

Q: Q2. Derive the equation of motion and find the natural frequency of vibration of the system shown in…

A: 7

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: Derive the differential equation characterizing the motion of an oscillation system subject to…

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Q: Find the velocity of a free vibration with a response of 4(d^2 x/dt^2) + 25x = o when t = 2.5s.…

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Q: 2. Find the natural frequency of vibration of a spring-mass system arranged on an inclined plane, as…

A: This problem is related with the basic mechanical vibration. Equation of natural vibration will be…

Q: Find the velocity of a free vibration with a response of 4(d^2 x/dt^2) + 25x = 0 when t = 2.5s.…

A: 2nd order differential equation is solved subjected to initial boundary condition to get the…