Problem $3)$

Consider a mass$-$spring system as shown in Fig. $1.$ A mass $\backslash ($ M $\backslash )$ is connected to a spring. The spring stiffness $\backslash ($ k $\backslash )$ depends on time $\backslash ($ t $\backslash )$ as

$\backslash [$

k$($t$)=$t

$\backslash ]$

a$)$ Write a differential equation for the above system. Comment on this equation.

b$)$ Solve this equation for $\backslash ($ M$=1\backslash )$ and no external force applied.