Experimenting with a Pendulum: Damping & Plotting Graphs

[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.

 

[HallsofIvy]

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= e^rt, 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 e^at(D₁cos(bt)+ D₂sin(bt)). You must have some initial conditions to determine D₁ and D₂.

 

[amppatel]

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

 

[amppatel]

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