Question

two bars of masses m1 and m2 connected by a non-deformed light spring,rest on a horizontal plane.the coefficient of friction between the bars and the surface is equel to x.if p is the minimum constant force to be applied in the horizontal direction to the bar of mann m1 in order to shift the other bar then p is equal to what

Answer 1

Hello mate here is your answer.

So,note that, when  is fix, and , under the influence of the spring,  moves like a damped harmonic oscillator. The amplitude of the first-half period (from left to right, for example) satisfies:
,
where,  is the spring constant. It is clear to see that the spring will be extended as long as in this process, which leads the maximum force, exerts on.

And thus we have:

So, the minimum value of , is given as:

namely,





Hope it helps you.