Differential equation with laplace transform and springs

Sneakatone
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Homework Statement


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

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
 
SteamKing said:
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?
 
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Sneakatone said:
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.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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