These demonstrations are arguably beyond the H2 syllabus. Nevertheless, they are fun and they may help you understand the H2 syllabus.

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Barton’s Pendulum

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The Quarter-cycle Lag between Driver-Driven

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The Tuning Fork Resonance

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The Coupled Pendulum

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The Coupled Inverted Pendulum

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The Tacoma Narrows Bridge

These 17 oscillations are arranged (from left to right) according to their angular frequency ω in ascending order. See the resulting pattern!

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Here is a physical demonstration using pendulum of increasing length.

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The supposed link between angular velocity (circular motion) and angular frequency (of oscillation).

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How does damping affect the amplitude of forced oscillations? Here is a demonstration.

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Here is an explanation.

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And here is an applet.

🍏: click here.

For an 🍏, click here

Suspension systems are designed to be critically damped.

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Skyscrappers are inverted pendulums that must be damped.

 

 

Here is a video showing you how to derive the energy-displacement formula at the snap of the finger!

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Animation of the energy-displacement graphs.

Remember that KE+PE=constant=TE

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Remember this: there are TWO energy cycles in each oscillation.

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Animation of the KE-time graph.

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Animation of the PE-time Graph

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Animation of the TE-time graph

Work done by Restoring Force increases KE.

Work done against Restoring Force increases PE.

Every pendulum is “born” with a natural frequency. This frequency (and period) is not affected by the amplitude of oscillation.

The natural frequency of a spring-mass system depend on the stiffness (the spring constant of the spring) and the inertia (the mass of the mass) of the system.

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The formula for the spring-mass system can be derived in just a few lines from N2L.

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The natural frequency of a pendulum is dependent only on its length. (The acceleration of free fall is the other factor, but we usually cannot choose the value of g.)

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Very intricate patterns can be traced out by a “double pendulum”. See the pendulum showing off its artistic streak below.

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The CRO (cathode ray oscilloscope) goes artistic too.

The restoring force keeps the mass accelerating towards the equilibrium position. The inertia (of the mass) causes the mass to always overshoot the equilibrium position. Hence the eternal karma of oscillations.