The spring$-$mass oscillator shown below has a mass $\backslash ($ m$=8\backslash$mathrm$\{$~kg$\}\backslash ),$ and a spring constant $\backslash ($ k$=\backslash )\backslash (72\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}.$ x $\backslash )$ is the displacement of the mass from its equilibrium position.

a$.$ Find a differential equation in $\backslash ($ x $\backslash )$ that describes the motion of the oscillator. $($You do not need to solve the differential equation.$)$

b$.$ Find $\backslash (\backslash$tau $\backslash ),$ the period of oscillation.