Harmonic Oscillators in Context (AQA A Level Physics) : Revision Note
Harmonic Oscillators in Context
Any oscillations about an equilibrium where its restoring force is proportional to its displacement will be simple harmonic
For example, liquid in a U-tube

Liquid in a U-tube is a type of simple harmonic oscillator with a displacement x from the equilibrium position and length L
The time period for these oscillations is found using the same equation as the time period of a simple pendulum
Where l is the known length of the liquid column
Worked Example
Water of length 20 cm is added to a U-tube. When added the water oscillates in simple harmonic motion in a time period T.

Calculate the frequency of the oscillations.
Answer:
Step 1: List the known quantities
L = 20 cm = 0.20 m
Step 2: From the data booklet
T =
Step 3: Rearrange time period equation for the frequency
f =
f =
Step 4: Substitute values into the frequency equation, to calculate f:
f = 1.11 Hz
Examiner Tips and Tricks
Don't let these slightly unusual situations confuse you. Try to model each part with each part against a conventional spring or pendulum system.
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