Defining Simple Harmonic Motion (SHM) - AP Physics 1

$T = 2\pi \sqrt{\frac{L}{g}}$. Period depends only on length and gravitational acceleration.

Kinetic energy and potential energy. Energy continuously transforms between these two forms during oscillation.

Radians per second (rad/s). This measures how fast the phase angle changes over time.

Hertz (Hz). Named after Heinrich Hertz, it represents cycles per second.

$f_0 = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$. This is the frequency at which the system naturally oscillates.

It reduces the amplitude and can eventually stop the motion. Energy is gradually lost to friction and other dissipative forces.

$T = \frac{2\pi}{\omega}$. These quantities are inversely proportional to each other.

Gravity acts as the restoring force. The component of weight provides the restoring force for pendulums.

The period increases. Longer pendulums oscillate more slowly due to increased inertia.

$K = \frac{1}{2}mv^2$. Kinetic energy is maximum when passing through equilibrium position.

Kinetic energy and potential energy. Energy continuously transforms between these two forms during oscillation.

The restoring force must be proportional to displacement. This linear relationship creates the characteristic sinusoidal motion pattern.

The equilibrium position is where the net force is zero. At this point, the object experiences no acceleration.

The period increases with mass. Heavier masses oscillate more slowly due to greater inertia.

The period decreases. Stiffer springs cause faster oscillations with shorter periods.

Damping is the reduction of amplitude over time. Friction and air resistance cause energy loss over time.

Determines the initial angle at $t=0$. It shifts the entire motion pattern in time.

The phase constant determines the initial position and direction. It sets the starting conditions at time zero.

$T = 2\pi \sqrt{\frac{L}{g}}$. Period depends only on length and gravitational acceleration.

Hooke's Law: $F = -kx$. This is the fundamental equation describing elastic force behavior.

$x(t) = A\cos(\omega t + \phi)$. This cosine function describes position as a function of time.

$\omega = \sqrt{\frac{k}{m}}$. This relates the system's physical properties to oscillation rate.

Frequency is the number of oscillations per unit time. It measures how many complete cycles occur in one second.

The length of the pendulum and gravity. Mass of the pendulum does not affect the period.

$\omega t + \phi = 0 \text{ or } \pi$. At these phases, velocity is zero and displacement is maximum.

The object moves back and forth about an equilibrium position. This repetitive motion is the defining characteristic of SHM.

$U = \frac{1}{2}kx^2$. Potential energy is maximum at maximum displacement positions.

$E = \frac{1}{2}kA^2$. Total energy is conserved and proportional to amplitude squared.

$a(t) = -A\omega^2\cos(\omega t + \phi)$. Acceleration is the time derivative of velocity in SHM.