IB Physics SL C.1.2 SHM defining equation

Use the defining SHM equation to read signs, compare positions and extract angular frequency from acceleration-displacement data.

Exam points

use the gradient of an acceleration-displacement graph to obtain -omega^2, then find f
apply a = -omega^2x to compare acceleration magnitude and sign at labelled displacements
use x-t or a-t graphs to identify that displacement and acceleration are pi out of phase

[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.1.2—SHM defining equation question 1 — IB Physics SL

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

D has mass $6.5 \times 10^{-3} \mathrm{~kg}$ and vibrates with amplitude 0.85 mm .

Calculate the maximum acceleration of D .

$\quad \omega=(2 \pi f=2 \pi \times 1250) 7854 \mathrm{rad} \mathrm{s}^{-1}$ ;

a_{0}=\left(-\omega^{2} x_{0}=-7854^{2} \times 0.85 \times 10^{-3}=\right)(-) 5.2 \times 10^{4} \mathrm{~ms}^{-2} ;

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C.1.2—SHM defining equation question 1