In class we analyzed an RC circuit with component values are
R=10k\Omega
and
C=100\mu F
. Here we will change the forcing function and the initial condition. a. Derive an expression for
v_(out )(t)
where
v_(out )(t)=v_(C)(t),v_(in )(t)=5sin(\omega t)V
, and
v_(c)(0)=v_(0)
i. Written solutions for the Laplace Transform (you can use the table) ii. A short description of what method/program you use to solve the inverse transform (if you use a website include the FULL url of the solution). b. What is the time constant for this system? How does this compare to
R=100k\Omega
and
C=100\mu F
? c. Plot the response of the system to the unit step input assuming zero initial conditions (make sure that your plot is well-formatted).