Differential equation with laplace transform and springs

[Sneakatone]

Homework Statement

I do not know how to find f(t) with the given Ampliture 40 and a=pi

Homework Equations

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)

 

[SteamKing]

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:

http://academic.udayton.edu/LynneYengulalp/Solutions219/LaplacePeriodicSolutions.pdf

 

[LCKurtz]

Homework Statement

I do not know how to find f(t) with the given Ampliture 40 and a=pi
View attachment 76100

Homework Equations

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)

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

 

[Sneakatone]

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:

http://academic.udayton.edu/LynneYengulalp/Solutions219/LaplacePeriodicSolutions.pdf

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

 

[LCKurtz]

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

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