A body of mass m kg attached to a spring moves with friction. The motion is desc

Question

A body of mass m kg attached to a spring moves with friction. The motion is described by the second Newton's law: md2y/dt2 + ady/dt + ky = 0, where y is the body displacement in m, t is the time in s, a > 0 is the friction coefficient in kg/s and k is the spring constant in kg/s2. Assuming m = 1 kg and k = 4 kg/s2, find: What is the range of values of a for which the body moves (i) with oscillations, (ii) without oscillations? Find the general solution for any a

Explanation / Answer

Yp=-a/2m +/-sqrt{(a/2m)^2-(k/m)} a) for no oscillation sqrt part must be greater than zero thus(a/2m)^2>(k/m) a^2>4(km) >16 a:(-infinity,-4) U (4,infinity) for oscillation a:(-4,4) b)y=A[e^[-a/2m]t]*e^[-sqrt[(a/2m)^2-(k/m)}]t for a=4 y=Ae^[-2t] as t-> infinity y->0 jus use the equation i have given above use a=4 n then put nitial condition simple i cant make a plot here i and please rate this answer well ths time i solved so much only for u..pls thanks if u need just need c part post only c separately

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