What is the equation a = −ω²x telling you?

The acceleration is proportional to displacement and in the opposite direction.

How are T, f and ω related?

T = 1/f = 2π/ω, and ω = 2πf.

What is the maximum speed in SHM?

vmax = Aω, at the equilibrium position.

What is the maximum acceleration in SHM?

amax = Aω², at maximum displacement.

Give the period of a simple pendulum.

T = 2π√(l/g), for small angles.

Does the period of a pendulum depend on the mass of the bob?

No. The mass cancels out of the equation.

What happens to the period of a mass-spring system if the mass is quadrupled?

It doubles, because T is proportional to √m.

Why must a pendulum swing through small angles for SHM?

Only for small angles does sin θ ≈ θ, so the restoring force is proportional to displacement.

Simple harmonic motionEdexcel International A Level Physics: Flashcards

Card 1 of 140 of 14 known

Question

State the condition for simple harmonic motion.

Tap or press Space to reveal

Tap card or press Space to flip

See all 14 cards

State the condition for simple harmonic motion.: The resultant force is proportional to the displacement from equilibrium and directed towards it: F = −kx.
What is the equation a = −ω²x telling you?: The acceleration is proportional to displacement and in the opposite direction.
How are T, f and ω related?: T = 1/f = 2π/ω, and ω = 2πf.
Give the equation for displacement in SHM starting at maximum displacement.: x = A cos ωt
Give the equation for velocity in SHM.: v = −Aω sin ωt
Give the equation for acceleration in SHM.: a = −Aω² cos ωt
What is the maximum speed in SHM?: v_max = Aω, at the equilibrium position.
What is the maximum acceleration in SHM?: a_max = Aω², at maximum displacement.
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.
Does the period of a pendulum depend on the mass of the bob?: No. The mass cancels out of the equation.
What happens to the period of a mass-spring system if the mass is quadrupled?: It doubles, because T is proportional to √m.
Why must a pendulum swing through small angles for SHM?: Only for small angles does sin θ ≈ θ, so the restoring force is proportional to displacement.
Which mode must a calculator be in for x = A cos ωt?: Radian mode.

Exam questions on Simple harmonic motion

A trolley of mass 0.40 kg rests on a horizontal, frictionless track. It is attached to a fixed support by a spring that obeys Hooke's law, with spring constant 25 N m⁻¹. The trolley is pulled 6.0 cm from its equilibrium position and released.
Explain why the trolley moves with simple harmonic motion after it is released.2 marks
A particle oscillates with simple harmonic motion with an amplitude of 4.0 cm and a frequency of 2.5 Hz. At time t = 0 it is at its maximum positive displacement.
Calculate the maximum speed and the maximum magnitude of the acceleration of the particle.2 marks
A student compares the oscillations of a mass on a spring with those of a simple pendulum. The mass-spring system consists of a mass of 0.250 kg suspended from a spring of spring constant 40 N m⁻¹. Use g = 9.81 m s⁻².
Calculate the period and the frequency of oscillation of the mass-spring system.3 marks

See the full worksheet

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).