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C.1.3—SHM quantities

Syllabus
First assessment 2025
Objective
—
Level
SL

Describe the Quantities in SHM

Name each quantity

The equilibrium position is the central position where the resultant restoring force is zero. Displacement xx is the signed distance from equilibrium. Amplitude x0x_0 is the maximum magnitude of displacement.

Connect time measures

The period TT is the time for one complete cycle. Frequency ff is the number of cycles per second, so T=1/fT=1/f. Angular frequency is ω=2πf=2π/T\omega=2\pi f=2\pi/T, measured in radians per second.

Keep amplitude and displacement distinct

Amplitude is a non-negative fixed maximum for an ideal oscillation; displacement changes continuously between −x0-x_0 and +x0+x_0. The sign of displacement identifies the side of equilibrium.

Common trap

Do not call the distance travelled in one cycle the amplitude. Amplitude is measured from equilibrium to an extreme position, not from one extreme to the other.

C.1.3 Exam Analysis

Assessment in practice

1–2 marks
How it is assessed

Questions ask you to read amplitude from a diagram or calculate a speed using amplitude and frequency. The evidence rewards selecting the maximum displacement correctly and converting the cycle information consistently.

Command terms

State / What is

What earns marks

Define the equilibrium position, displacement x, amplitude x0, period T, frequency f and angular frequency ω separately. Use T = 1/f and ω = 2πf, and do not confuse amplitude with peak-to-peak distance or total path length.

Watch for

Reading peak-to-peak displacement as the amplitude instead of taking the distance from equilibrium to one extreme.

Representative question

Question 1

[Maximum number: 1]

State the amplitude of the motion.

Retrieve the Core C.1 Simple Harmonic Motion Model

Recognize SHM

SHM requires a restoring acceleration a=−ω2xa=-\omega^2x about equilibrium. Track displacement, amplitude, period, frequency and angular frequency with T=1/f=2π/ωT=1/f=2\pi/\omega.

Track one cycle

At an extreme, potential energy is maximum and kinetic energy is zero; at equilibrium, kinetic energy is maximum and potential energy is minimum. Total energy remains constant in ideal SHM.

Read the motion

The gradient of a displacement–time graph is velocity. Acceleration is opposite to displacement. Use the sign of displacement and the gradient to identify direction at any instant.

Final check

Measure displacement from equilibrium, keep amplitude distinct from peak-to-peak distance, and name the relevant potential-energy form for the oscillator.