Forced Oscillations (Resonance)

  

Forced sinusoidal oscillations of a spring pendulum (red circle).

Click on the "Reset" button to return to the default values. Use the "Start" / "Stop" / "Resume" buttons to control the simulation. "Slow motion" slows the simulation down by a factor of 5. The spring constant, attached mass, attenuation constant, frequency of the exciting oscillation can be changed within certain limits.
In addition you can select among three diagrams by using the appropriate radio buttons:

    *  The elongations of exciter and resonator as functions of time
    *  The amplitude of the resonator's oscillation dependent on the exciter's angular frequency
    *  The phase difference between the oscillations of exciter and resonator dependent on the exciter's angular frequency

Three different types of behavior may be observed:

_ If the exciter's frequency is lower than the characteristic frequency of the spring pendulum, the pendulum will oscillate nearly synchronously with the exciter and with nearly the same amplitude.

_ If the exciter's frequency is near or equal to the characteristic frequency of the spring pendulum, the oscillations of the pendulum will build up to the highest possible amplitudes (resonance) and will be delayed by ~ 1/4 period relative to the exciter.

_ If the exciter's frequency is higher than the characteristic frequency of the spring pendulum, the resonator will oscillate at a very low amplitude and will be delayed ~ by 1/2 period relative to the exciter.

The smaller the attenuation constant (friction), the longer the transient states and the longer the time it will take for the above mentioned behaviors to be observed.