1: Mass (m), 2: Spring (k), 3: Equilibrium position.

1: Length (L), 2: Mass (m), 3: Angle of displacement ($\theta$).

Periodic motion where the restoring force is proportional to the displacement from equilibrium.

The force that always directs toward the equilibrium position and is proportional to the displacement ($F = -kx$).

The maximum displacement of the object from its equilibrium position.

A measure of how rapidly the oscillations occur, related to the period (T) by $\omega = \frac{2\pi}{T}$.

The time it takes for one complete cycle of the motion.

It represents the initial position of the oscillating object at time t=0.

Take the first derivative of the position function with respect to time: $v(t) = \frac{dx(t)}{dt} = -A\omega \sin(\omega t + \phi)$.

Take the first derivative of the velocity function with respect to time: $a(t) = \frac{dv(t)}{dt} = -A\omega^2 \cos(\omega t + \phi)$.

Use the formula: $T = 2\pi \sqrt{\frac{m}{k}}$, where m is the mass and k is the spring constant.

Use the formula: $T = 2\pi \sqrt{\frac{L}{g}}$, where L is the length of the pendulum and g is the acceleration due to gravity.

Sum the kinetic and potential energies: $ME = K + U$, where $K = \frac{1}{2}mv^2$ and $U = \frac{1}{2}kx^2$ (for a spring) or $U = mgh$ (for gravity).