# Differential equation with laplace transform and springs

1. Dec 2, 2014

### Sneakatone

1. The problem statement, all variables and given/known data
I do not know how to find f(t) with the given Ampliture 40 and a=pi

2. Relevant equations

3. The attempt at a solution
I have the solution above.

my set up was 1/2y''+y'+5=f(t)

1/2S^2* Y(s) + Y(s)+5=f(t)

2. Dec 2, 2014

### SteamKing

Staff Emeritus
Have you studied periodic functions? Do you know how to obtain the Laplace transform of a periodic function?

Here is a brief article discussing how:

Last edited by a moderator: May 7, 2017
3. Dec 2, 2014

### LCKurtz

You want the LaPlace transform of f(t) on the right of that last equation. To see how to get the transform of a periodic function, look here:
http://www.intmath.com/laplace-transformation/5-transform-periodic-function.php

4. Dec 2, 2014

### Sneakatone

From the looks of this does amplitude not matter , only the period?

Last edited by a moderator: May 7, 2017
5. Dec 2, 2014

### LCKurtz

Wrong. There is an $f(t)$ in the formula for the transform, so everything about $f(t)$ matters.