HW #$4$

Due October $23,2024,$ at $11$:$59$PM by submitting on Canvas.

For all problems, you can assume gravity is $9\mathrm{.}81\frac{m}{?}$

This problem uses MATLAB. Turn in your program and plots, as well as answers to the following parts. Please print your MATLAB code as a pdf to include in your submission. Be sure to include axis labels with units and legends with your plots.

Consider the spring$-$damper system shown, where and the spring is initially at rest with $x(0)=0m.$

$3-1.(10$ pts$)$ Derive a first$-$order linear differential equation to describe the position of the spring with applied force $F(t).$

$3-2.(5$ pts$)$ Assuming that $F(t)$ is a constant value of $F,$ determine the particular solution to the spring position, $x(t).$

$3-3.(pts)$ Provide equations which describe: $(1)$ the energy stored in the spring as a function of time $U(t)$ and $(2)$ the power dissipated by the damper as a function of time, $P(t)$