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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).