Defining Simple Harmonic Motion (SHM) - AP Physics C: Mechanics

The length of the pendulum. Length determines the period of oscillation.

$U = \frac{1}{2} k A^2$. All energy is potential when kinetic energy is zero.

Large amplitude oscillations when frequency matches natural frequency. Driving frequency equals natural frequency for maximum energy transfer.

Total mechanical energy. No energy is lost to friction or other dissipative forces.

Reduction of amplitude over time due to resistive forces. Friction and air resistance cause energy loss over time.

Energy transitions between kinetic and potential forms. Kinetic and potential energy oscillate while total remains constant.

Radians per second (rad/s). Measures rate of phase change in oscillatory motion.

$\omega = 2\pi f$. Angular frequency is frequency multiplied by $2\pi$.

Period decreases with increasing spring constant. Stiffer springs produce faster oscillations.

Period increases with mass. Heavier objects oscillate more slowly due to greater inertia.

$T = 2\pi\sqrt{\frac{L}{g}}$. Valid only for small angular displacements (less than 15°).

$T = 2\pi\sqrt{\frac{m}{k}}$. Period is independent of amplitude in SHM.

Initial angle in the argument of the cosine or sine function. Determines starting position and velocity of the oscillation.

$\omega = \sqrt{\frac{k}{m}}$. Derived from $F = ma$ and $F = -kx$ for mass-spring systems.

Period decreases with increased gravity. Stronger gravity increases restoring force and frequency.

For small angular displacements. Small angle approximation makes restoring force proportional to displacement.

$\frac{\pi}{2}$ or 90 degrees. Velocity leads position by 90°, acceleration leads velocity by 90°.

Large amplitude oscillations when frequency matches natural frequency. Driving frequency equals natural frequency for maximum energy transfer.

Radians per second (rad/s). Measures rate of phase change in oscillatory motion.

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

$v(t) = -A\omega \sin(\omega t + \phi)$. Velocity is the time derivative of position.

Energy transitions between kinetic and potential forms. Kinetic and potential energy oscillate while total remains constant.

Period decreases with increasing spring constant. Stiffer springs produce faster oscillations.

Reduction of amplitude over time due to resistive forces. Friction and air resistance cause energy loss over time.

$\frac{1}{2\pi}\sqrt{\frac{k}{m}}$. Frequency when system oscillates freely without external forces.

Angle $\theta$ must be less than 15 degrees. Ensures $\sin(\theta) \approx \theta$ for linear restoring force.

Radians. Phase has no physical dimensions.

Position where the net force is zero. Reference point where restoring force equals zero.

Frequency at which a system oscillates when not disturbed. Characteristic frequency determined by system properties only.