IB Physics SL C 1 Simple Harmonic Motion Questions

Practise IB Physics SL C.1 by linking a = −ω²x to displacement graphs, tracking motion with amplitude and period, and comparing kinetic and potential energy across a cycle.

Exam points

Use a = −ω²x to identify SHM and interpret the negative gradient of an acceleration–displacement graph.
Use amplitude and period to calculate displacement at a stated fraction of an SHM cycle.
Read displacement–time graphs to identify turning points and locate maximum acceleration using a = −ω²x.
Convert between T, f and ω, then infer a missing period or frequency from oscillation data.
Use kinetic-energy graphs to compare kinetic and potential energy at key points in an SHM cycle.

Covered syllabus points

C.1.1—Conditions for SHM C.1.2—SHM defining equation C.1.3—SHM quantities C.1.4—Period, frequency and angular frequency C.1.5—Mass–spring period C.1.6—Simple pendulum period C.1.7—Qualitative energy changes in SHM

[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.

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

(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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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question 2

Question (a)

Question (b)

Question (c)

Question (d)