IB Physics SL C.1.1 Conditions for Simple Harmonic Motion

Practise proving that an oscillation is simple harmonic by showing a resultant acceleration proportional to displacement and directed back towards a stable equilibrium position.

Exam points

identify the equilibrium position and show the resultant force reverses when displacement reverses
derive or state F = -kx or a = -ω²x, with the negative sign indicating restoration
reject SHM when the force is not proportional to displacement or points away from equilibrium

[Maximum number: 2]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

Figure for Question C.1.1—Conditions for SHM question 1 — IB Physics SL

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Define simple harmonic motion (SHM).

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C.1.1—Conditions for SHM question 1