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A 3kg object is attached to spring and will stretch the spring 392mm by itself. There...

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Physics

A 3kg object is attached to spring and will stretch the spring392mm by itself. There is no damping in the system and a forcingfunction of F(t)=10 coswt, w=(k/w)-2 is attached to theobject. The spring is deflected y distance father than equilibriumposition due to the F(t). k is the spring modulus and M is the massof the object.

a) Derive the governing equation for the spring-object masssystem decribed in the problem.Assume Mg=hk

b) if the object is initially displaced 20cm downward from itsequilibrium position and given a velocity of 10cm/s upward find thedisplacement of the object at any time t.

c) suppose a damper is added to the mass-spring system that willexert a force of 45N when the velocity is 50cm/s, damping factor of90kg/s is added to the system. And find the displacement of theobject at any time t for this new system

d)Determine the amplitude , nature frequency and phase shift ofthe object for this new system.

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