Undamped Forced Oscillations -- Beats
by Mike Martin

Consider an undamped spring-mass system with external sinusoidal forcing:

m x '' + k x = Fo cos(ω t)

Suppose further that the mass is initially at rest at it's equilibrium position:

x (0) = 0, x ' (0) = 0

The natural frequency of the system is ωo = (k / m)1/2 and the forcing frequency is ω. We assume on this page that the natural frequency of the system and the forcing frequency are not equal. The frequencies can be close in value, but not equal. Submit real values for the mass, m, the spring constant, k, the forcing amplitude, Fo, and the forcing frequency, ω. The solution is plotted on the interval [0, T], where the final time value, T, is input by the user.



Enter in the value of the parameters and select the plotting bounds, then press the "Plot" button.

m =  

k =  

F0 =  

ω =  

T =  


References:

MIT Lecture on Beats

Wikipedia's Beats(acoustics)