Find the response of a damped spring-mass system when a force F(t), as shown in Figure, acts onthe mass m. Assume k = 2500 N/m, c= 10 N-s/m, m = 0.25 kg, T= 2 sec and consider first threeharmonics.F(1)+12rTime tFigure

given data; ⇒stifness of spring (K)=2500N/m⇒mass(m)=0.25kg⇒time(τ)=2sec⇒damping…

Answered: Find the response of a damped…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.
Q3.Consider a spring–mass–damper system with m = 80 kg, c = 15 kg/s, and k = 1500 N/m with an impulse force applied to it of 1200 N for 0.01 s. (C) Calculate the damped natural frequency of the system (D) Calculate the system response to the impulsive force at time t = 1 s
Consider a spring-mass-damper system with k=4000N/m, m=10kg,and c=40N-s/m Find the steady-state and total response of the system under harmonic force F(t)=200 cos t N and the initial conditions x0=0.1m and ̇x0'=0
The structure shown in figure has a mass of 100 kg and a translational stiffness of 40,000 N/m. It is excited by a harmonic force having an amplitude Po = 500 N and an excitation frequency ω = 15 rad/s. The damping factor for the structure is ξ = 0.1. The initial conditions are u(0) = 6 cm and ώ(0) = 0. For the steady-state vibration determine: (a) The amplitude of the stady-state displacement. (b) Its phase with respect to the exciting force. (c) The maximum velocity and acceleration of the response. (d) Determine the equation that describes the total displaement of the structure as a function of time.
A weight of mass 2 kg is placed on a long vertical spring with spring constant k = 20. The damping force is 4 dy/dt Newtons. The weight is moved 2 meters above its equilibrium position and is started in motion with a velocity of 1 meter/sec. upward. Find the equation of motion for the weight. (There is no external force).
A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is released from a point 10 cm below its equilibrium position with an upward velocity of 15 cm/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to twelve times the instantaneous velocity. Find the position function (the equation of motion) if the mass is driven by an external force f(t)=40cos(5t).
In the figure, a disk-shaped wheel of mass M and radius R rolls without slipping on a circular platform of radius 2L+R. The wheel is attached by a torsion spring to a pendulum of length 2L of mass m and moves with this pendulum.a) Derive the differential equation for the motion of the system given here.b) Find the natural frequency of the free motion of the system. L=2 [m], R= 0,5 [m], m=5 [kg], M= 65[kg], kb= 165 [Nm/rad] Note: There is no friction in this system
A mass m is attached to two identical springs having constant k as shown in the figure. What is the natural frequency ∞ of this single degree of freedom system?
Find the period and make a graph of "xv/s t", of a mass-spring system with elastic constant K=8 Kg/s² and m=2 Kg, which moves from its equilibrium position ma, distance d = 0.5m . Make a graph of damped and undamped.
A spring-mass system with m = 50kg and k = 4000N/m shown in Figure Q3(a).If the mass is released from its equivalent position and results in simpleharmonic motion (SHM),(i) Starting from a free body diagram, derive the equation of motion.(ii) Determine the natural frequency. (iii) Explain on how you can reduce the natural frequency of the spring-masssystem.
Figure 1 shows a system comprising a bar with mass m-12 kg and the length of the bar L=2 m, two springs with stiffness kt=1000 N-m/rad and k = 2000 N/m, one damper with damping coefficient c=50 N-s/m and two additive masses at the end of the bar, where each mass (M) is equal to 50 kg. The rotation about the hinge A, measured with respect to the static equilibrium position of the system is 0 (t). The system is excited by force (F) so find the state space representation of the system if the output y=ġ(t).
A block-spring system has a maximum restoring force Fmax = 0.1 N. If the amplitude of the motion is A = 0.01 m and the mass of the block is m = 100 g then the angular frequency w is equal to

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Find the response of a damped spring-mass system when a force F(t), as shown in Figure, acts on the mass m. Assume k = 2500 N/m, c = 10 N-s/m, m = 0.25 kg. T= 2 sec and consider first three harmonics. F1) +1 2r Time t Figure