A cart of mass $0\mathrm{.}338$ kg is placed on a horizontal track. A spring with a spring constant of $8\mathrm{.}15\frac{N}{m}$ is attached between the cart and the left end of the track. The cart's initial position compresses the spring to $x_L=-0\mathrm{.}120m$ from its equilibrium position $($let $x_0=0m).$ The cart is released and allowed to oscillate $($without friction$)$ between $x_L$ and $x_R.$

a$)$ Find the period at which the cart oscillates. $(2$ points$)$

b$)$ Find the cart's maximum speed. $(2$ points$)$

c$)$ Find the cart's speed when it is located $0\mathrm{.}0700m$ from its equilibrium position. $(2$ points$)$