What does the minus sign in a = −ω²x mean?

The acceleration is always in the opposite direction to the displacement, towards equilibrium.

How are period, frequency and angular frequency related?

T = 1/f = 2π/ω, so ω = 2πf.

Give the equations for velocity and acceleration in SHM.

v = −Aω sin ωt and a = −Aω² cos ωt.

What is the maximum speed in SHM and where does it occur?

Aω, at the equilibrium position.

What is the maximum acceleration in SHM and where does it occur?

Aω², at maximum displacement (the ends of the motion).

Give the period of a simple pendulum.

T = 2π√(l/g), for small angles only.

What setting should the calculator be in for SHM equations?

Radians, because ωt is in radians.

Simple harmonic motion and its equationsEdexcel A-Level Physics: Flashcards

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State the condition for simple harmonic motion.

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State the condition for simple harmonic motion.: The resultant force (or acceleration) is proportional to the displacement from equilibrium and directed towards it.
Write the defining equation of SHM in terms of acceleration.: a = −ω²x.
What does the minus sign in a = −ω²x mean?: The acceleration is always in the opposite direction to the displacement, towards equilibrium.
How are period, frequency and angular frequency related?: T = 1/f = 2π/ω, so ω = 2πf.
Give the equation for displacement in SHM, starting from maximum displacement.: x = A cos ωt.
Give the equations for velocity and acceleration in SHM.: v = −Aω sin ωt and a = −Aω² cos ωt.
What is the maximum speed in SHM and where does it occur?: Aω, at the equilibrium position.
What is the maximum acceleration in SHM and where does it occur?: Aω², at maximum displacement (the ends of the motion).
Give the period of a mass on a spring.: T = 2π√(m/k).
Give the period of a simple pendulum.: T = 2π√(l/g), for small angles only.
Does the period of a pendulum depend on the mass of the bob?: No, only on the length and g.
What setting should the calculator be in for SHM equations?: Radians, because ωt is in radians.

Exam questions on Simple harmonic motion and its equations

A trolley of mass 0.40 kg is attached to a horizontal spring of spring constant 25 N m⁻¹. The other end of the spring is fixed. The trolley is pulled 0.060 m from its equilibrium position along a frictionless track and released. It then oscillates with simple harmonic motion.
Calculate the maximum speed of the trolley.2 marks
A simple pendulum consists of a small dense bob on a light string. The distance from the pivot to the centre of the bob is 1.50 m. The bob is displaced through a small angle and released. The gravitational field strength is 9.81 N kg⁻¹.
Calculate the period and the frequency of the pendulum.2 marks
A loudspeaker cone vibrates with simple harmonic motion. Its displacement x from the equilibrium position is given by x = A cos ωt, where the amplitude A is 0.12 m and the frequency is 2.5 Hz. Time t = 0 is when the cone is at its maximum positive displacement.
Calculate the angular frequency of the vibration and the displacement of the cone 0.050 s after t = 0.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).