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Study C.1 Simple harmonic motion conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 6]

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.

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

(a)

Define simple harmonic motion (SHM).

[ 2 ]

(b)

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

[ 4 ]

(i)

Calculate the maximum acceleration of D .

[ 2 ]

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

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

(ii)

Determine the total energy of D .

[ 2 ]

correct substitution into $E_{T}=\frac{1}{2} m \omega^{2} x_{0}{ }^{2}$ irrespective of powers of 10 ;

0.14 \text { to } 0.15 \mathrm{~J} ;

[Maximum number: 8]

This question is in two parts. Part 1 is about simple harmonic motion and forced oscillations. Part 2 is about electric and magnetic force fields.

Part 1 Simple harmonic motion and forced oscillations
The graph shows the variation with time of the displacement of an object undergoing simple harmonic motion.
displacement / mm

time / ms

(a)

State the amplitude of the oscillation.

[ 1 ]

(b)

Calculate the frequency of the oscillation.

[ 2 ]

period $=160 \mathrm{~ms}$ ;
frequency $=6.2 / 6.3 \mathrm{~Hz}$ ;

Marking guidance:

Allow ECF for incorrect period.

(c)

Determine the maximum speed of the object.

[ 2 ]

$\quad \omega=2 \pi \times 6.25$ ;
$v\left(=39.3 \times 32 \times 10^{-3}\right)=1.3\left(\mathrm{~m} \mathrm{~s}^{-1}\right) ;($ allow ECF from (a))
or
tangent drawn to graph at a point of zero displacement;
gradient calculated between 1.2 and 1.4;

(d)

The graph below shows how the displacement of the object varies with time. Sketch on the same axes a line indicating how the kinetic energy of the object varies with time. You should ignore the actual values of the kinetic energy.

[ 3 ]

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IB Physics SL C 1 Simple Harmonic Motion Topic Practice

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Question 1

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Question (b)

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Question (ii)

Question 2

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Question (b)

Question (c)

Question (d)