C.1 Simple harmonic motion questions for IB Physics

83 questions on Simple harmonic motion, written by Augment in the style of IB exam papers. Six of them are below in full, to answer on paper.

IB Physics
Part of C Wave behaviour
SL and HL

Questions by paper and level

SL and HL questions are for students at either level. HL only questions cover what only HL students study.

Paper	SL and HL	HL only	All
Paper 1A	22	13	35
Paper 1B	6	0	6
Paper 2	23	19	42
Every paper	51	32	83

Counted on 10 November 2026

Questions to try

Written by Augment in the style of IB exams, not past papers. Answer them on paper, then check each one against its markscheme with a free account.

Question 1 · PHY-00555Paper 1A · 1 mark

A buoy floating in a harbour is pushed down a short distance and released. It bobs up and down. The motion of the buoy is simple harmonic if the resultant force on it is

A
proportional to its displacement from the equilibrium position and directed towards that position.
B
proportional to its displacement from the equilibrium position and directed away from that position.
C
constant in magnitude and always directed towards the equilibrium position.
D
proportional to its speed and directed opposite to its velocity.

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Question 2 · PHY-01106Paper 1B · 10 marks

A group of students investigate resonance. A mass of 0.200 kg hangs from a spring attached to a vibration generator. A signal generator makes the vibration generator oscillate vertically with frequency $f$ and a small constant amplitude. The students measure the amplitude $A$ of the oscillations of the mass against a vertical metre rule. The uncertainty in $A$ is $\pm 0.2 cm$ .

A vibration generator clamped at the top of a stand is connected to a signal generator. A spring hangs from the vibration generator with a mass at its lower end. A vertical metre rule stands beside the mass.

The students then fix a light horizontal card to the mass and repeat the experiment. The graph shows the variation of $A$ with $f$ for both arrangements.

Graph of amplitude A in cm (0 to 9) against driving frequency f in Hz (1.1 to 2.1) with error bars of 0.2 cm. Without the card: a sharp peak of about 7.9 cm near 1.59 Hz. With the card: a low, broad curve with a maximum of about 1.8 cm near 1.56 Hz.

(a)
State the resonant frequency of the system without the card.
1 mark
(b)
Assume that the natural frequency of the mass–spring system is equal to your answer to (a). Calculate the spring constant of the spring.
2 marks
(c)
Calculate the percentage uncertainty in the maximum amplitude when the card is used.
1 mark
(d)
Describe the effect of the card on the variation of $A$ with $f$ .
2 marks
(e)
Outline why the card has this effect.
1 mark
(f)
Suggest how the students could determine the resonant frequency more precisely using the same apparatus.
1 mark
(g)
The mass is replaced by one of 0.300 kg and the card is removed. Predict the new resonant frequency.
2 marks

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Question 3 · PHY-00400Paper 2 · HL only · 10 marks

A block of mass 0.380 kg rests on a horizontal air track and is attached to a fixed support by a spring of spring constant 40 N m $^{- 1}$ . The spring is at its natural length. A dart of mass 0.020 kg moving horizontally at 15 m s $^{- 1}$ along the axis of the spring hits the block and sticks in it. Friction is negligible.

A spring fixed to a support on the left is attached to a block on a horizontal air track. A dart moves horizontally to the left towards the block along the axis of the spring.

(a)
Calculate the speed of the block and dart immediately after the collision.
2 marks
(b)
Calculate the percentage of the dart's initial kinetic energy that is transferred to other forms in the collision.
2 marks
(c)
The block and dart then oscillate with simple harmonic motion. Calculate the period of the oscillations.
2 marks
(d)
Determine the amplitude of the oscillations.
2 marks
(e)
Calculate the maximum force exerted on the block by the spring, and the maximum acceleration of the block.
2 marks

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Question 4 · PHY-00556Paper 1A · 1 mark

Three systems are set oscillating:

I. a steel ball bouncing vertically on a hard floor with no loss of energy
II. a trolley held between two stretched springs on a horizontal frictionless track, displaced along the line of the springs
III. a simple pendulum swinging through a small angle

Which systems perform simple harmonic motion?

A
I and II only
B
I and III only
C
II and III only
D
I, II and III

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Question 5 · PHY-01134Paper 1B · 11 marks

A group of students investigates how the period of oscillation of a glider on a horizontal air track depends on the mass it carries. The glider is attached between two identical stretched springs whose other ends are fixed to the ends of the track. Friction is negligible.

A horizontal air track with a glider in the middle. A stretched spring joins the left end of the track to the glider and another joins the glider to the right end. A slotted mass sits on top of the glider.

The students add slotted masses of total mass $m$ to the glider. For each value of $m$ they displace the glider along the track, release it and use a stopwatch to measure the time $10 T$ for ten oscillations, where $T$ is the period.

$m$ / kg	$10 T$ / s ± 0.2 s
0.050	10.1
0.100	11.2
0.150	11.9
0.200	12.9
0.250	13.6
0.300	14.3

The theory of the arrangement predicts that

T = 2 π \sqrt{\frac{M + m}{k}}

where $k$ is the combined spring constant of the two springs and $M$ is a constant mass.

The graph shows the variation of $T^{2}$ with $m$ , with error bars for $T^{2}$ and the line of best fit.

Graph of T squared in seconds squared (0 to 2.4) against m in kilograms (0 to 0.35). Six points with vertical error bars of about plus or minus 0.05 rise from 1.02 at 0.050 kg to 2.05 at 0.300 kg. A straight best-fit line passes through them and meets the T squared axis at about 0.83.

(a)
Outline why the students time ten oscillations rather than one.
1 mark
(b)
Calculate the percentage uncertainty in $T^{2}$ for $m = 0.050 kg$ .
2 marks
(c)(i)
Determine, using the graph, $k$ .
3 marks
(c)(ii)
State the unit of the gradient of the graph.
1 mark
(d)(i)
Determine $M$ .
2 marks
(d)(ii)
The mass of the glider, measured on a balance, is 0.180 kg. Suggest why $M$ is greater than this value.
1 mark
(e)
Suggest one change to the procedure that would reduce the uncertainty in $T$ , using the same apparatus.
1 mark

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Question 6 · PHY-00488Paper 2 · 10 marks

Carbon dioxide molecules absorb infrared radiation strongly at two wavelengths, 15 μm and 4.3 μm. Each absorption corresponds to a transition between vibrational energy levels of the molecule.

(a)
Calculate, in eV, the energy of a photon of wavelength 15 μm.
2 marks
(b)
Show that the difference between the energy levels for the absorption at 4.3 μm is about 0.3 eV.
1 mark
(c)
In a resonance model of this vibration, an oxygen atom of mass 16 u oscillates on a spring of stiffness $k$ attached to a fixed carbon atom. The natural frequency of this oscillator equals the frequency of radiation of wavelength 4.3 μm.
Determine $k$ .
3 marks
(d)
Infrared radiation of a range of frequencies is incident on the molecule. Sketch a graph to show how the amplitude of the oscillation of the molecule varies with the frequency of the incident radiation. Label the natural frequency $f_{0}$ on the frequency axis.
2 marks
(e)
Water vapour is the most abundant greenhouse gas. Suggest why the water vapour released by human activities has little direct effect on the greenhouse effect, while warming caused by carbon dioxide increases the amount of water vapour in the atmosphere.
2 marks

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