Category: 08 Simple Harmonic Motion

8.B More Demonstrations

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

Bartonโ€™s Pendulum

explanation at xmdemo

The Quarter-cycle Lag between Driver-Driven

explanation at xmdemo

The Tuning Fork Resonance

explanation at xmdemo

The Coupled Pendulum

explanation at xmdemo

The Coupled Inverted Pendulum

explanation at xmdemo

The Tacoma Narrows Bridge

explanation click here

8.A Angular Frequency vs Angular Velocity

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

explanation at xmdemo

Here is a physical demonstration using pendulum of increasing length.

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

8.2.1 Natural Frequency

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.

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

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.)

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

explanation at xmdemo

The CRO (cathode ray oscilloscope) goes artistic too.

explanation at xmdemo

8.2 Restoring Force

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.