Simple harmonic motion
x = A cos(omega t) and a = -omega2 x
The sign gives the direction: SHM acceleration always points back towards equilibrium.
Know the equation
| Symbol | Quantity | Unit |
|---|---|---|
| x | displacement from equilibrium | m |
| A | amplitude | m |
| omega | angular frequency | rad/s |
| t | time | s |
| a | acceleration | m/s2 |
Rearrangements
- A = x / cos(omega t)
- omega = 2 pi f = 2 pi / T
- x = -a / omega2
- omega = sqrt(-a / x)
Apply it — mark your own working
Work each one out on paper first, then reveal the mark scheme and tick the marks you actually earned. That is exactly how you should mark past papers.
An oscillator has amplitude 0.080 m and frequency 2.5 Hz. At t = 0 it is at maximum positive displacement. Calculate its displacement at t = 0.12 s.
Do the calculation on paper first — then mark it.
A particle oscillates with frequency 4.0 Hz. At one instant its displacement is +0.035 m. Calculate its acceleration at that instant.
Do the calculation on paper first — then mark it.
Where the marks get lost
- Using frequency f in place of angular frequency omega; convert with omega = 2 pi f first.
- Dropping the minus sign in a = -omega2 x, which loses the restoring-direction physics.
- Using degrees mode for cos(omega t); omega t is an angle in radians.
Exam tip: State the sign of your answer. A negative displacement is a position on the negative side; a negative acceleration means the acceleration points in the negative direction.
Still losing marks on the calculations?
I'll go through your working line by line and show you exactly where the marks are — your first lesson is free.