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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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.
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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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