(a) displacement, amplitude, period, frequency, angular frequency and…

The idea

These six quantities describe any oscillation. Displacement x is the signed distance from the equilibrium position, so it is negative on one side and positive on the other. Amplitude A is the maximum magnitude of displacement, always positive. Period T is the time for one complete cycle, measured in seconds. Frequency f is the number of cycles per second, f = 1/T, in hertz. Angular frequency ω converts cycles to radians per second: ω = 2π/T = 2πf, so a 2.0 Hz oscillation has ω = 2π × 2.0 = 4π rad s⁻¹ ≈ 12.6 rad s⁻¹. Phase difference φ compares two oscillations of the same frequency, expressed in radians or degrees; a quarter-cycle lag is π/2 rad or 90°.

What earns the marks

• Displacement is a signed vector-like quantity measured from the equilibrium position, not the total distance travelled.
• Amplitude is the maximum magnitude of displacement and is always positive.
• Period T is the time for one complete oscillation, measured in seconds.
• Frequency f = 1/T is the number of complete oscillations per second, measured in hertz.
• Angular frequency ω = 2π/T = 2πf, measured in rad s⁻¹.
• Phase difference compares the timing of two oscillations of the same frequency, in rad or degrees.

Common mistakes and how to put them right

• Confusing displacement with distance travelled.

  Put it right: Displacement is signed and measured from equilibrium, whereas distance travelled accumulates and is never negative.

• Treating amplitude as a signed quantity.

  Put it right: Amplitude is the maximum magnitude of displacement and is always positive.

• Using ω = 2πT instead of ω = 2π/T.

  Put it right: Check that a larger period gives a smaller angular frequency.

• Expressing phase difference in seconds.

  Put it right: Phase difference is an angle in radians or degrees, not a time.

Exam tips

• Write the defining relationship for each quantity before substituting numbers, so the examiner can see your reasoning.
• Check units carefully: T in s, f in Hz, ω in rad s⁻¹, phase difference in rad or degrees.
• When comparing two oscillations, confirm they have the same frequency before quoting a phase difference.