Reference: MATLAB for Engineering Applications, by William Palm. McGraw$-$Hill, $5$th Edition.

The equation of motion for a pendulum whose base is accelerating horizontally with an acceleration $a(t)$ is

$L{}^{}+$gsin$=a(t)cos$

Suppose that $g=9\mathrm{.}81\frac{m}{s^2},L=1m,$ and ${}^{}(0)=0.$ Plot $(t)$ for $0t10s$ for the following three cases.

a$.$ The accelerathon is constant: $a=5\frac{m}{s^2},$ and $(0)=0\mathrm{.}5$rad.

b$.$ The acceleration is constant: $a=5\frac{m}{s^2},$ and $(0)=3$rad.

c$.$ The acceleration is linear with time: $a=0\mathrm{.}5t\frac{m}{s^2},$ and $(0)=3$rad. Matlab and dont use chat gpt