A particle $($mass $=0\mathrm{.}5)$ oscillates in simple harmonic motion $($in $1$D$)$ with an amplitude of $0\mathrm{.}05$ meters and an oscillation period of $0\mathrm{.}25\mathrm{????}.$

$$a$)$ Find the frequency of oscillation. $$ Write a "coordinate function" $\mathrm{????}(\mathrm{????}),$ that describes these oscillations about equilibrium. What initial position and initial velocity did you choose?

b$)$ Sketch $\mathrm{????}(\mathrm{????})$ for $2$ oscillations. Similarly sketch $\mathrm{????}(\mathrm{????}).$

$$c$)$ Find $\mathrm{????}(\mathrm{????})$ and show that the acceleration is directly proportional to the displacement.

d$)$ Find the system's effective "spring constant" stiffness.

e$)$ Find the particle's KE$,$ PE and ME$.$