Motion where the restoring force is proportional to displacement and acts in the opposite direction.

The back-and-forth movement of an object around its equilibrium position.

The maximum displacement from the equilibrium position.

Time for one complete cycle of motion. Measured in seconds.

Number of cycles per second. Measured in Hertz (Hz).

Force that pulls an object back to its equilibrium. Always points towards equilibrium.

Measure of a spring's stiffness. Higher k means a stiffer spring.

Rate of oscillation in radians per second. $ω = 2πf = \frac{2π}{T}$

Initial angle of the oscillation at t=0. Determines the starting position.

When an object vibrates with maximum amplitude because of an external force at its natural frequency.

Increasing the mass increases the period of oscillation.

Increasing the spring constant decreases the period of oscillation.

Increasing the length increases the period of oscillation.

Increasing gravity decreases the period of oscillation.

Resonance occurs, causing a dramatic increase in amplitude.

1. Identify the mass (m) and spring constant (k). 2. Use the formula: $T = 2π\sqrt{\frac{m}{k}}$

1. Identify the length of the pendulum (L) and the acceleration due to gravity (g). 2. Use the formula: $T = 2π\sqrt{\frac{L}{g}}$

1. Identify the spring constant (k) and amplitude (A). 2. Use the formula: $U_{max} = \frac{1}{2}kA^2$

1. Identify the mass (m) and maximum velocity (v_max). 2. Use the formula: $K_{max} = \frac{1}{2}mv_{max}^2$

1. Find either the maximum potential energy (U_max) or the maximum kinetic energy (K_max). 2. Total energy: $E = U_{max} = K_{max}$