Undamped Forced Oscillations -- Resonance
by Mike Martin

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

m x '' (t) + k x (t) = 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 equal and examine the resulting response. Submit real values for the mass, m, the spring constant, k, and the forcing amplitude, Fo. The solution is plotted on the interval [0, T], where the final time value, T, is input by the user. x (t) represents the displacement of the mass at time t.

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

m =  

k =  

Fo =  

T =  


MathWorld's Simple Harmonic Oscillator

Wikipedia's Harmonic Oscillator

Wikipedia's Simple Harmonic Motion

Wikipedia's Resonance