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

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.

[2]

Answer:

Step 1: List the known quantities

• Length of water, $L=20\mathrm{cm}=0.20\mathrm{m}$

• Gravitational field stength, $g=9.81\mathrm{N}{\mathrm{kg}}^{-1}$

Step 2: From the data booklet

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

$T=2\pi \sqrt{\frac{L}{g}}$

Step 3: Rearrange time period equation for the frequency

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

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

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

$f=\frac{1}{2\pi }\sqrt{\frac{9.81}{0.20}}$ [1 mark]

$f=1.11\mathrm{Hz}$ [1 mark]

Don't let these slightly unusual situations confuse you. Try to model each part against a conventional spring or pendulum system.