the world in a different light
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:
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).
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.
I created this simulation for use later this semester with my IP4 classes, to illustrate the concept of phase difference between two oscillating particles.
https://ejss.s3-ap-southeast-1.amazonaws.com/phasedifference_Simulation.xhtml
Update (26 August 2020): I have also created a GeoGebra app to demonstrate the same principle.
This is the Pendulum Clock from the LEGO Education Simple and Powered Machines Set. It can be used to demonstrate the variation of period with length of pendulum and is a very good visual representation of the escapement mechanism.
There are many other models that one can build using this set, including a weighing scale, elastic energy powered car, etc. All with potential for class demonstrations.
You can buy a set from Duck Learning in Singapore at (S$329.75), an exclusive distributor of LEGO Education products in Singapore. If you are purchasing in bulk for your school, you may want to contact them directly for a package deal. You can also purchase them from overseas sites such as Bricklink.com if you can find them at a better price.
This is a video that we usually will show during a lecture on the topic of Resonance, under the unit “Oscillations”. It was taken in 1940 at the Tacoma Narrows Bridge in Washington, USA. One of the main reasons (not the only reason – the other being aeroelastic flutter) for its collapse is the effect of resonance, which occurs when the driving frequency of the wind that hits the bridge matches the natural frequency of vibration of the bridge.