Test $3$

MCEG $4306-$ Dynamic Systems and Controls

November $6,2024$

Use MATLAB to find Laplace transforms $($add your name in script file$)$:

$f(t)=3sint-cos{}^{2}t+15e^{-t}$

$20\%$ Use MATLAB to find Laplace transforms of the following time functions $($add your name in script file$)$:

$f(t)$ is the time function shown in the graph.

$10\%$

Use MATLAB to find the time function from its corresponding Laplace transform $($add your name in script file$)$:

$\frac{6w}{2s^2+50w^2}5s^2+5w^2$

$60\%$

$4.$ A sinusoidal force acts on the mass$-$damper$-$spring mechanical system as shown in the figure. The parameters $m_1=2kg,m_2=10kg,k=3000\frac{N}{m},$ and $c=20N\frac{s}{m}.$

The amount force transmitted to the Wall will vary when input force changes its frequency $.$ We define:

Magnitude $(\frac{?}{abs})=$ the ratio between force transmitted to Wall and input force Fsin$(t).$ Phase $(deg)=$ phase angle of the dynamic response.

You are required to derive the equations for the dynamic system $($must be uploaded$),$ Use MATLAB to make a bode plot for Magnitude $($abs$)$ and Phase $($deg$)$ verses $,$ and Add a title 'Your Name Bode Plot' to your bode plot.