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).

Increasing the mass increases the period (T).

Increasing the spring constant decreases the period (T).

Increasing the length increases the period (T).

Increasing gravitational acceleration decreases the period (T).

The velocity is at its maximum value.

The acceleration is at its maximum value and directed towards the equilibrium position.