A LevelPhysicsAQARevision NotesFurther Mechanics & Thermal PhysicsSimple Harmonic MotionHarmonic Oscillators in Context

Harmonic Oscillators in Context (AQA A Level Physics): Revision Note

Exam code: 7408

Written by: Ashika

Updated on 2 July 2026

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

U-tube SHM, downloadable AS & A Level Physics revision notes

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

$T = 2 π \sqrt{\frac{l}{g}}$

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.

q3a_oscillations_ib-sl-physics-sq-medium

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 = $\frac{1}{f}$

$f = 2 π \sqrt{\frac{L}{g}}$

Step 3: Rearrange time period equation for the frequency

f = $\frac{1}{T}$

f = $\frac{1}{2 π}$ $\sqrt{\frac{g}{L}}$

Step 4: Substitute values into the frequency equation, to calculate f:

$f = \frac{1}{2 π} \sqrt{\frac{9.81}{0.20}}$

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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