Drag the object to change the amplitude.
The slider for damping adjusts the value of \(\frac{\gamma}{2 \omega}\) and defaults to 0 (no damping).
When the slider value is set to 1, the system is critically damped. A value greater than or less than 1 represents the cases of over-damping and under-damping respectively. Observe the difference among the three different cases of damping.
The calculations below is updated the moment the simulation is paused.

Drag on the ball to change the length.
Drag on the bar to change the angle.
Click on the clock to reset the timer.
The mass of the object is fixed to be \(m = 1kg\).
The grey horizontal line represents the lowest level of the pendulum trajectory, used as a reference level for height measurement.

Activity

Use the clock to time 10 oscillations and deduce the period. Repeat for a different length and see how the period changes.

Graph of Simple Harmonic Oscillation

General solution to $\ddot{y} = - \omega^2 y$:

Graph of Resonance with Mass on a Spring

The graph is the amplitude of the oscillator in response to the driving frequency and damping coefficient.

Phase Difference of Forced Oscillations

The driving force (top graph) and the actual oscillation (bottom graph) are not in phase in general (in plain English: they do not rise and fall together at the same time). For example, during resonance (when the driving frequency equals the natural frequency), the two graphs should be off by $\pi/2 rad$ (or $90^\circ$). If you look carefully, you can see the peak of one graph coincides with the zero of the other at resonance. Away from resonance, the phase difference takes different values.