MATLAB Project - Elbow

Consider the following mechanism, consisting of a crank AP and a lever PB loosely hinged at the “elbow” P so that it can bend only to the right. The end A is hinged to a fixed point 8 cm above an origin O. The crank AP has length 5 cm, and the lever PB has length 12 cm. The end B is able to slide back and forth along the x-axis in a harmonic fashion with amplitude 15 cm and period 2 sec, such that

$x \left(t\right)=15 \cos \pi t$,  $t$ ≥ 0.

At any given instant t ≥ 0, let θ(t) (“theta”) denote the angle of rotation of the crank AP, measured in a clockwise direction from the upper vertical.

Let φ(t) (“phi”) be the angle at the elbow P, as shown.