# Harmonic Oscillator Activities

Install Ejs and then right-click on a launch node (green arrow) to copy the Free Fall model from this package into the Ejs workspace to do the following activities.

### Period

Measure the period of the motion for the given initial conditions. Drag with the mouse the ball to a new position and measure the period again. How does the period of the oscillation depend on the initial displacement?

Double the mass. By what factor does the period change? Quadruple the mass and repeat.

### Friction

The model assumes that energy is conserved. Modify the differential equation to include energy loss due to air friction. This energy loss can be modeled by including a friction (drag) force Ffriction that is proportional to the velocity:

Ffriction= - b v .

The drag coefficient b depends on the shape of the object and should be included in the model as an additional variable. A good value for simulation is b/m =0.1 although realistic values for objects in air is lower.

### Energy

Add a plot showing the kinetic energy, potential energy, and total energy to the model.