Simple harmonic motion (SHM) (A-level only) Flashcards – AQA A-level Physics (7408)

What defines simple harmonic motion (SHM)?

Oscillatory motion in which acceleration is proportional to displacement from equilibrium and directed towards equilibrium.

What is the defining equation for acceleration in SHM?

$a=-\omega^2x$, where $x$ is displacement from equilibrium and $\omega$ is angular frequency. The minus sign indicates opposite directions.

For SHM starting at maximum positive displacement, what is displacement as a function of time?

$x=A\cos(\omega t)$, where $A$ is the amplitude.

For SHM starting at maximum positive displacement, what is velocity as a function of time?

$v=-\omega A\sin(\omega t)$

For SHM starting at maximum positive displacement, what is acceleration as a function of time?

$a=-\omega^2A\cos(\omega t)$

What does the gradient of a displacement–time graph represent?

Velocity.

What does the gradient of a velocity–time graph represent?

Acceleration.

How does the phase of velocity compare with that of displacement in SHM?

Velocity is a quarter cycle ahead of displacement.

How does the phase of acceleration compare with that of displacement in SHM?

Acceleration is in antiphase with displacement.

What is the relationship between velocity and displacement in SHM?

$v=\pm\omega\sqrt{A^2-x^2}$. The sign depends on the direction of motion.

What is the speed at equilibrium in SHM?

It is greatest: $v_{\max}=\omega A$.

What is the velocity at either extreme of SHM?

Zero.

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

$a_{\max}=\omega^2A$, at either extreme: $x=\pm A$.