Section 12
Oscillations and periodic motion
Frequency is the reciprocal of the period.
Angular frequency is 2π times the frequency.
Position in simple harmonic motion, of amplitude A and initial phase φ.
For a mass–spring system
In SHM, the acceleration is opposite to the displacement and proportional to it.
Also
Velocity in simple harmonic motion; its square is ω²(A²−x²).
Angular frequency of a mass-spring system, equal to the square root of k/m.
Equivalent form
Period and frequency of a mass-spring oscillator.
The total energy of SHM is constant and equal to (1/2)kA².
The maximum speed in SHM is the product of the amplitude and the angular frequency.
The maximum acceleration in SHM is the product of the amplitude and the square of the angular frequency.
Angular frequency of a simple pendulum, equal to the square root of g/L.
- small-angle approximation, .
Equivalent form
Period and frequency of a simple pendulum.
- small oscillations.
Equivalent form
Period of a physical pendulum, determined by the moment of inertia and the distance to the center of mass.
Equivalent form
Equivalent form
Oscillator whose restoring torque is proportional to the angle; the angular frequency is the square root of κ/I.
Note: is used for the torsional constant, to avoid confusing it with the constant of a linear spring.