10 Oscillations

Pendulum-Powered Car

This pendulum-powered car is constructed using Lego Technic parts. I used mainly Lego beams to create the chassis and an “A” frame from which the pendulum is suspended. The pendulum is made of Lego beams and some wheels.

When the pendulum swings, it experiences an acceleration towards its equilibrium position. By the principle of conservation of momentum, the car experiences a change in momentum in the opposite direction. Since the acceleration of the pendulum changes its direction every half a cycle of its oscillation, the car will only oscillate about its original position if the wheels of the car are free to turn throughout the oscillation. 

A escapement mechanism which consists of a beam resting on a pair of 40-tooth gears attached to the front wheels prevent the wheels from rotating in the opposite direction. This means that the car will only be moving forward during the half of the pendulum’s oscillation when its displacement is at the front of its equilibrium position and pauses during the other half.

Escapement mechanism to keep the pendulum car moving in one direction

Simple harmonic motion graphs including energy

I have added two more graphs into the interactive animation. However, the app has become a bit sluggish when changing the period or amplitude. It still works smoothly when viewing the animation.

Students ought to find it useful to look at all the graphs together instead of in silo. This way, they can better understand the relationships between the graphs.

As usual, here is the animated gif file.

Simple Harmonic Motion Graphs

Here’s my attempt at animating 5 graphs for simple harmonic motion together in one page.

From left column:

$$v = \pm\omega\sqrt{x_o^2-x^2}$$

$$a = -\omega^2x$$

From right column:

$$s = x_o\sin(\omega t)$$

$$v = x_o\omega \cos(\omega t)$$

$$a = -x_o\omega^2 \sin(\omega t)$$

And here is the animated gif file for powerpoint users:

Simple harmonic motion graphs - displacement-, velocity-, acceleration- time graphs and more

Box on a Vertical Oscillating Spring – Geogebra App

GeoGebra link: https://www.geogebra.org/m/ev62ku7w

Students can explore how varying frequency and amplitude of the vertical oscillation of a platform could cause an object resting on it to temporarily leave the platform (i.e. when normal contact force is zero).

Velocity-Displacement Graph of a Simple Harmonic Oscillator – Animation

This animation is made using Geogebra. It shows the instantaneous velocity and displacement vectors of a particle undergoing simple harmonic motion while tracing its position on the velocity-displacement graph. It is meant to help student understand why the graph is an ellipse.