Question

A particle of mass m can perform undamped harmonic oscillations due to an electric force with coefficient k. When the particle was in equilibrium, a permanent force F was applied to it for τ seconds. Find the oscillation amplitude that the particle acquired after the action of the force ceased. Draw the approximate plot x (t) of oscillations. Investigate possible cases.

Answer 1

We have to look for solutions of the equation

Subject to  where F is constant.

The solution of this equation will be sought in the form

A and α will be determined from the boundary condition at t = 0. 

B and β will be determined by the continuity of x and x at t = τ. Thus