$(30$ points$)$ Imagine that a pendulum with mass $m$ and length $1$ is swinging with a small amplitude on a cart. The pendulum and cart are being loaded on a truck by pushing them up a ramp $($incline has angle $$ and total height $h)$ at a constant speed v$.$ Find the oscillatory motion of the pendulum while it is being loaded by using Lagrange's equation and solving the resulting differential equation$($s$).$ Does the loading process affect the frequency of the pendulum? Explain.