Dynamic Systems II Mechanical Engineering

$($a$)$ You are given a system that can be modeled as a $1^{st}$ order, homogeneous, linear, constant coefficient ODE of the form:

$a_1{y}^{}+a_{0}y=0$

When released from an initial displacement, the system behaves as shown below. $($Hint: at time $t=0,y=81\mathrm{.}54)$

Now, find the time constant $({}_c)$ and the coefficients of the equation that describes this system. $($Note: the exponential decay can be written as $y(t)=C{e}^{pt}$

${}_c=$

$p=$

$C=$

$($b$)$ Is p negative or positive? Explain.