Q2: For mass-spring system shown. The mass is given an initialdisplacement x(0)= 0.1 m, and released from rest. Find:1- The position of the mass after 2 seconds.2- The velocity of the mass after 2 seconds.3- Plot the response for three cycles and label the result from 1 & 2.4- What is the period of oscillation?5- What is the acceleration of mass (m) after 5 second?Įx(t)k=100 N/mm = 4 kg

The stiffness of the springMass of the blockInitial displacementIt is released from the rest so the…

Answered: Q2: For mass-spring system shown. The…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Damped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k b
3. A 100-pound weight is suspended from a vertical spring whose module is 100 pounds per foot. The weight is pulled downward 9 inches from its equilibrium position and released. Viscous fluid exerts 20 Ibs of force when the plunger moves through it at 0.5 ft/sec; 3.a What is the damping condition? Write the equation which describes the motion of the weights. Show graph. 3.b displacement 3.c velocity 3.d acceleration
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The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation. k₁ k₂ K3 K= - (K₁ + K₂) k₂ m₁ = 1, m₂ = 5; k₁ = 3, k₂ = 15, k3 = 15 k₂ - (K₂ + K3) Describe the mode of oscillation for w₂. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The two masses move linearly, staying a fixed distance apart. B. The two masses oscillate in the same direction, where the amplitude of m₁ is O C. The two masses oscillate in opposite directions, where the amplitude of m₁ is D. The two masses oscillate in the same direction with equal amplitudes. E. The two masses oscillate in opposite directions with equal amplitudes. times the amplitude of m2. times the amplitude of m₂.
5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X; measures horizontal ground motion and co-ordinate X measures the position of the mass m relative to the frame of the seismograph. The mass m = 1 kg, the spring stiffness k = 10 Nm-1 and the coefficient of the damper c = 2 Nsm-¹. Starting from rest, the seismograph is subjected to an oscillatory ground motion given by X; = (10sin2t) mm. For the mass m, (a) set up the equation of motion, (b) calculate the amplitude of the steady state response, and (c) develop an equation describing the amplitude of steady state oscillation as a function of time. To Figure Q5 m
For the shown spring-mass-damper system. Let m =1 kg, b = 2 N.s/m, k = 2 N/m and t) = sin2t N. (a) Write the equation of motion. (b) Find the amplitude of the steady state oscillations. (c) In steady state, find the time delay in seconds between the mass position and (t).
A spring has an unstretched length of 12 cm. When an 80 g ball is hung from it, the length increases by 4.0 cm. Then the ball is pulled down another 4.0 cm and released.a. What is the spring constant of the spring?b. What is the period of the oscillation?c. Draw a position-versus-time graph showing the motion of the ball for three cycles of the oscillation. Let the equilibrium position of the ball be y = 0. Be sure to include appropriate units on the axes so that the period and the amplitude of the motion can be determined from your graph.
Task 1 For the shown spring-mass-damper system. Let m =1 kg, b = 2 N.s/m, k =2 N/m and ft) = sin2t N. (a) Write the equation of motion. (b) Find the amplitude of the steady state oscillations. (c) In steady state, find the time delay in seconds between the mass position and At). (d) Find the steady state maximum acceleration.
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Q3: Draw the free-body diagram and derive the equation of motion (EOM) using: (1) Newton's 2nd law (2) Energy method for the systems. (3) Find the natural frequency. m 4r 1447 x(t) k 00000 -Pulley, mass moment of inertia Jo
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s

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