IB Physics SL C.1 Simple harmonic motion Questions

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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.

58 questions in this syllabus scope, with question parts counted together.

Exam points & syllabus

Exam points

State both SHM conditions: acceleration or net restoring force is proportional to displacement from equilibrium and acts in the opposite direction.
Connect an SHM model to its restoring mechanism and range: Hooke’s-law springs, a supplied small piston motion or a partially submerged constant-section float.
Interpret an acceleration–displacement graph by its origin and gradient: proportionality gives a straight line, and the restoring sign gives a negative slope.
Distinguish signed acceleration from its magnitude; at an extreme velocity is zero and |a| is largest, while equilibrium gives a=0 and greatest speed.
For the same oscillation, compare |a| in proportion to |x|; on a wave profile use the particle offset, not its position along the wave.
Find period from a full repeat of the same state and direction, convert timing units and use T=1/f=2π/ω.
Use a measured restoring coefficient or acceleration–displacement slope to find ω, then convert to frequency or period with the 2π factor.
For a mass–spring oscillator, combine T=2π√(m/k) with the actual effective stiffness; equal springs and equal periods imply equal masses.
Use T=2π√(l/g) for a small-angle simple pendulum; its period is independent of bob mass and grows when g decreases at fixed length.
Measure amplitude from equilibrium to an extreme; use quarter-cycle symmetry and total distance 4A to calculate average speed over a cycle.
Read or sketch motion graphs using slopes, turning points and initial direction; a velocity graph need not share the sign of the displacement graph.
For a qualitative v–x choice, check both directions at each interior displacement and zero velocity at both extremes before accepting a closed curve.
Use graphical kinematics when the scheme supports it: quarter-cycle area under v–t gives amplitude, and a steepest x–t tangent gives maximum speed.
Count complete oscillations on a recording trace and use elapsed time=N/f; uneven spatial spacing can reflect recorder motion rather than changing frequency.
Describe energy exchange through the cycle: kinetic energy is zero at turning points and greatest at equilibrium; potential energy changes oppositely.
For an ideal oscillator, total energy stays constant while kinetic and potential energy repeat twice per displacement cycle and remain non-negative.
When a potential-energy curve is supplied, read the total energy at the turning point and sketch kinetic energy as its difference from that supplied curve.

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: 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.

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).

Define simple harmonic motion (SHM).

[Maximum number: 2]

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).

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} ;

[Maximum number: 1]

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

State the amplitude of the oscillation.

[Maximum number: 3]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Simple harmonic motion and waves

One end of a light spring is attached to a rigid horizontal support.

An object W of mass 0.15 kg is suspended from the other end of the spring. The extension x of the spring is proportional to the force F causing the extension. The force per unit extension of the spring k is $18 \mathrm{Nm}^{-1}$ .

A student pulls W down such that the extension of the spring increases by 0.040 m . The student releases W and as a result W performs simple harmonic motion (SHM).

Determine the period of oscillation of the spring.

$\omega=\sqrt{\frac{a}{x}}$ ;
$=10.95 \mathrm{rads}^{-2}$ ;

T=\left(\frac{2 \pi}{\omega}=\right) \frac{6.28}{10.95}=0.57 \mathrm{~s} ;

[Maximum number: 2]

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).

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

Determine the total energy of D .

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: 2]

This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring.

Part 1 Solar radiation and the greenhouse effect
The following data are available.

(a)

The sketch graph below shows how the displacement of the object from point O varies with time over three time periods.

[ 2 ]

(i)

Label with the letter A a point at which the magnitude of the acceleration of the object is a maximum.

[ 1 ]

(ii)

Label with the letter V a point at which the speed of the object is a maximum.

[ 1 ]

[Maximum number: 1]

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

$\frac{T}{4}$

$\frac{T}{2}$

$\frac{3 T}{4}$

Question 1

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Question (a)

Question (i)

Question (ii)

Question 1