A body performs simple harmonic motion - AQA - A-Level Physics - Question 29 - 2018 - Paper 1

In simple harmonic motion, the displacement of a body can be expressed as:

$x(t) = A imes ext{cos}( heta)$

where:

• $A$ is the amplitude
• heta = rac{2 heta}{T} \times t, with $T$ being the period

The acceleration can be derived from the displacement equation using:

a(t) = -rac{d^2x}{dt^2} = -A \omega^2 \times ext{cos}( heta)

where:

• $heta$ again is related to time
• $\\omega$ is the angular frequency

In simple harmonic motion, the acceleration is always negative and is out of phase with the displacement by a phase difference of:

rac{ heta}{ ext{phase difference}} = \pi ext{ rad}

Thus, the phase difference between the variation of displacement and the variation of acceleration is:

Answer: $\pi$ rad