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# Solve Problems Using Laplace Transforms

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Calculate and graph the output voltage in the RL circuit of the above circuit if:

E(t) = k when t greater than or equal to 0 and less than 5

E(t) = 0 when t greater than or equal to 5

The current is initially 0

See attached file for full problem description.

https://brainmass.com/physics/partial-differential-equation/solve-problems-using-laplace-transforms-103585

#### Solution Preview

The sum of the potentials on the inductor and the resistor must be equal the potential of the source:

Since

The time dependent differential equation is:

Applying ...

#### Solution Summary

This solution provide step by step analysis for calculating and graphing output voltage.

\$2.19

## Solving a Laplace Transform Problem

Solve the following DE using Laplace Transform. Be sure to show your steps and reference the Laplace Transform you will be using. {i.e. - e^at sin bt; b/((s-a)^2 + b^2) (s > a) }

(d^2y)/(dt^2) + 2(dy/dt) + 2y = x(t)

where

x(t) = { 1, 0 < = t < = 1
x(t) = { 2, t > = 2
x(t) = { 0, elsewhere

and

y(0) = 0; y'(0) = 1

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