Simple Harmonic Motion

Simple Harmonic Motion

Simple Harmonic Motion (SHM) occurs when a restoring force is proportional to displacement (Hooke's law: $F = -kx$). The resulting motion is sinusoidal:

$x(t) = A \cos(\omega t)$

• $A$ — amplitude (maximum displacement, metres)
• $\omega$ — angular frequency (rad/s): $\omega = 2\pi f = 2\pi / T$
• $t$ — time (seconds)

Starting at $t = 0$, the object is at maximum displacement $x = A$.

Key Quantities

$T = \frac{2\pi}{\omega} qquad f = \frac{\omega}{2\pi}$

Velocity and Acceleration in SHM

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

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

The acceleration always opposes displacement — this is the hallmark of SHM.

Examples

Your Task

Implement shmX(A, omega, t) returning displacement in metres.