# Damped Pendulum

1. Aug 20, 2008

### amppatel

I am doing an experiment on the pendulum, and i wanted to do something on the damping, i understand a little as i have done some reading on it, the picture attached show the working i have done, i have reached a second order DE and i know little about this. So my question is, can you plot a graph? and how can you find out the damping co efficent, i have some results i have measured the amplitude every other half oscilation.

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• ###### Pendulum.jpg
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2. Aug 20, 2008

### HallsofIvy

Staff Emeritus
Okay, you have mx"+ (k/m)x'+ nx= 0. That's a linear homogeneous differential equation with constant coefficients, about the simplest possible equation. If you "try" a solution of the form x= ert, you arrive at the characteristic equation:
mr2+ (k/m)r+ n= 0. That is a quadratic equation and can be solved by the quadratic equation, giving r= a+bi and a- bi which means that the solutions to the differential equation are of the form C1e(a+ bi)t+ C2e(a-bi)t which can in turn be written eat(D1cos(bt)+ D2sin(bt)). You must have some initial conditions to determine D1 and D2.

3. Aug 20, 2008

### amppatel

ok so i get that, abit, but does that allow me to plot a curve? or can i solve the equation for k?

4. Aug 20, 2008

### amppatel

also eat(D1cos(bt)+ D2sin(bt)) what is that equal to? zero? Thanks for all your help