Problem $4$:

Consider the horizontal bar, pulley, and mass single$-$

dof system shown in the figure.

System is excited by $y(t)=$Asin$(t)$ from its

equilibrium position starting at $t=0.$ Assume small

oscillations. Treat pulley as a uniform disc with

mass, $m_d$ and radius $r.$

Use $m_1=1kg,L=1m,m_d=0\mathrm{.}25kg,r=$

$0\mathrm{.}1m,m_2=1kg,k_1=10\frac{N}{m},k_2=20\frac{N}{?}$

$m,c=10N\frac{s}{m}.$

$($a$)$ What is resonance frequency, ${}_{\text{r}\text{e}\text{s}},$ of this

system?

$($b$)$ If $A=0\mathrm{.}1m=10ra\frac{d}{s},$ what is the

amplitude of $x_1(t)$ for mass $m_2?$

$($c$)$ Using the excitation amplitude and the

frequency from part $($b$),$ find the steady$-$

state solution for $x(t).$