Problem $1$:

Consider the crank slider at right. The slider is aligned with the $y$ axis $($no offest$).$ The crank angular velocity magnitude is constant at ${}_2=100ra\frac{d}{s}($i$.$e$.,{}_2=0ra\frac{d}{s^2}).$ Perform the following tasks:

a$)$ Using Matlab, plot the $y$ position of the slider as a function of crank angular position ${}_2$ over one full rotation of the crank.

b$)$ Using Matlab, plot the $y$ component of the velocity of the slider as a function of crank angular position ${}_2$ over one full rotation of the crank.

c$)$ Using Matlab, plot the $y$ component of the acceleration of the slider as a function of crank angular position ${}_2$ over one full rotation of the crank.

d$)$ Comment on whether the slider $y$ position, velocity and acceleration are harmonic $($perfectly sinusoidal$)$ or not.

Please provide all of your work $($derivations$,$ Matlab code, final answers, etc.$).$