Chapter 4.P3, Problem 5P

Consider the case of an undamped problem $\left(\gamma =0\right)$ using the parameter values $L=1,m=1,k=1$ and initial conditions $x\left(0\right)=2,x^{\prime }\left(0\right)=0$. Find the solution $x\left(t\right)$ of the initial value problem for $0\le t\le t_1^{\ast }$ and $t_1^{\ast }\le t<t_2^{\ast }$, where $t_1^{\ast }$ and $t_2^{\ast }$ are the times of the first and second events. Describe the physical situation corresponding to each of these two events.