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In the figure shown, mass M is at rest, mass m the falls on mass M and adheres to it without any rebound, derive the equation of motion for this system and express the natural frequency of this system.

In the figure shown, mass M is at rest, mass m the falls on mass M and adheres to it without any rebound, derive the equation of motion for this system and express the natural frequency of this system.

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AE 510 HW 2 Name: For the figure shown, flnd the natural frequency of the system. 2. For the following systenm with m; = 2 kg, the period of oscillation is, T = 0.05 sec. When the mass m2 is added, the perlod is increased to 0.08 sec. Find the magnitudes of m2 and k. (3. In the figure shown, mass M is at rest, mass m the falls on mass M and adheres to it without any rebound, derive the equation of motion for this system and express the natural frequency of this system. sluy 4. An oscillatory system consists of a mass, m =120 a spring constant, k 40 lb/in, and a damping coefficient, c = 5 lb.sec/in. Find, (a) the natural frequency, (b) the damping ratio, (c) damped frequency. In problem 4, assume the initial condition to be, uo = 0.2 in, Vo = 0.5 in/sec, find the maximum deflection and plot the response, u(t). The response of a mass-spring-damper system is given in the figure, determine (a) the natural frequency of the system, (b) the logarithmic decrement, (c) the damping factor. 7. A projectile weighing 1 lb, moving straight at a speed of 500%sec as shown. This projectile strikes a mass 2 lb that is supported by a spring k = 10 lb/In and a damper 0.5 lb.sec/in. The projectile embeds in the mass. Find the equation of the motion after the system after impact.
Transcribed Image Text:AE 510 HW 2 Name: For the figure shown, flnd the natural frequency of the system. 2. For the following systenm with m; = 2 kg, the period of oscillation is, T = 0.05 sec. When the mass m2 is added, the perlod is increased to 0.08 sec. Find the magnitudes of m2 and k. (3. In the figure shown, mass M is at rest, mass m the falls on mass M and adheres to it without any rebound, derive the equation of motion for this system and express the natural frequency of this system. sluy 4. An oscillatory system consists of a mass, m =120 a spring constant, k 40 lb/in, and a damping coefficient, c = 5 lb.sec/in. Find, (a) the natural frequency, (b) the damping ratio, (c) damped frequency. In problem 4, assume the initial condition to be, uo = 0.2 in, Vo = 0.5 in/sec, find the maximum deflection and plot the response, u(t). The response of a mass-spring-damper system is given in the figure, determine (a) the natural frequency of the system, (b) the logarithmic decrement, (c) the damping factor. 7. A projectile weighing 1 lb, moving straight at a speed of 500%sec as shown. This projectile strikes a mass 2 lb that is supported by a spring k = 10 lb/In and a damper 0.5 lb.sec/in. The projectile embeds in the mass. Find the equation of the motion after the system after impact.
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