HW$3\mathrm{.}1.$ Manipulating and solving a first order system

Consider the system $a{v}^{}+bv=0$ which can be thought of as a mass$-$damper system where a represents the mass and $b$ represents

the damping in the system for the following questions:

Part A

Given the parameters $a=5kg$ and $b=3\frac{(kg)}{(s)}$ and an initial velocity, $v_o=10\frac{(m)}{(s)},$ determine $v(t)$ at $t=1sec.$

Note: First solve symbolically before plugging in values.

$v(1)=$ number rtol $=0\mathrm{.}01,$ atol $=1e-08$

Part B

Given an initial velocity, $v_o=7\frac{(m)}{(s)},$ determine the ratio $\frac{a}{b}sec$ such that $v(7)=2\frac{(m)}{(s)}.$

Note: First solve symbolically before plugging in values.

$\frac{a}{b}$

ec

Part C

The time constant of a first order dynamic system, $,$ is defined as the time at which the system's response is at $36\mathrm{.}8\%$ of its

initial condition. Determine the value of $$ for the system in Part A$.$