Simulation - Periodic Motion and Waves

Drag on the mass to change its position. Click "Play" to start the oscillation.

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

The Basics of Waves

Direction button: change wave direction
Longitudinal button: show/hide longitudinal wave

Doppler's Effect

Adjust the velocity of the source and see how it affects the wavefronts.
Gradually change the source velocity from below the speed of sound to above. Could you see any qualitative differences between the two cases?