# Simulation - Periodic Motion and Waves

## Hooke's Law

Canvas not supported
Drag on the mass to change its position. Click "Play" to start the oscillation.

## Spring Oscillations with Damping

Canvas not supported
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.
Calculations will appear here.

## Simple Pendulum

Canvas not supported

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

Canvas not supported
##### Graph of Simple Harmonic Oscillation
General solution to $\ddot{y} = - \omega^2 y$:
Calculations will appear here.

## The Basics of Waves

Canvas not supported

#### The Basics of Waves

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

## Doppler's Effect

Canvas not supported

#### 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?