PHY354H1 Lecture Notes - Damping Ratio, Fourier Series
Document Summary
Lecture 10: driven oscillations: relevant reading: morin 4. 4, oscillation dynamics when you have driving forces. Forced oscillations: consider a system that has restoring forces and damping forces but also has a driving force that is periodic. F (t) = f (t + t ) = f (t + 2t ) for some t . F0 m cos dt (1) with the idea that we can solve for any periodic forcing by expressing. F (t) as a fourier series and summing over the solutions: notice that the above equation is inhomogeneous. That means we are going to have to do something a little di erent to nd the solution. It turns out there are 2 pieces to the solution for inhomogeneous equa- tions. We call 1 part the particular solution xp and the other part the homogeneous solution xh . The general solution is then written: x = xh + xp.
