# Laplace Transforms

#### callum_ensor

Joined May 22, 2018
4
Hi Everyone
I’ve managed to get the first two questions, just really struggling on the last.
Anyone got an idea, it’s causing me a headache
Thankyou

#### Attachments

• 85.9 KB Views: 12

#### callum_ensor

Joined May 22, 2018
4

#### callum_ensor

Joined May 22, 2018
4
Working out so far...

Joined Mar 10, 2018
4,057
A quick check on your work is the following (in RC time constants) -

5 time constants get you to ~ 99% of the final value.

Just realized your input is a ramp, but its slow enough above should still
apply ?

Regards, Dana.

Last edited:

#### WBahn

Joined Mar 31, 2012
26,398
Your math in the first equation is not consistent. You units don't work out from the second line. And then the (CR2+1) factor magically transports itself from the left side to the right side at the bottom of the first column. Then it magically appears in the denominator of the last term at the top of the right column. This has all the hallmarks of being a solution that was forced to yield what you already knew the result was supposed to be.

#### WBahn

Joined Mar 31, 2012
26,398
A quick check on your work is the following (in RC time constants) -

5 time constants get you to ~ 99% of the final value.

Just realized your input is a ramp, but its slow enough above should still
apply ?

Regards, Dana.
If the ramp is slow compared to the time constant, the response will look like it tracks the ramp. If it is fast compared to the time constant, the response will look like a step response.

#### MrAl

Joined Jun 17, 2014
8,146
Hello there,

It looks like you might be applying a ramp in one question, although i cant seem to find that question here.

If you are, then the thing to do is look up the forcing function for a ramp and apply that instead of a step input. The result is a gradual increase followed by a ramp that looks delayed from the input.
If you are applying a ramp 'pulse' however, then when the ramp ends you have to start from there and change the forcing function to zerro and use the last results from the ramp as the initial conditions for the circuit. The result will be a capacitor diccharging as usual but with the initial voltage being the last voltage attained just before the ramp ended.

The general response for an RC circuit excited by a ramp with zero initial conditions is:
Vc(t)=a*R*C*e^(-t/(R*C))-a*R*C+a*t

where 'a' is the slope of the ramp. The final cap voltage Vc(t) can be used as the initial condition for the circuit if the ramp ends at some 't' where the input then falls to zero.

In the attachment, red is the input and blue is the cap voltage.