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Mechanics · Quick Reference
Oscillations Cheat Sheet
In one line: an oscillation is any repeating back-and-forth motion around a central equilibrium position — from a swinging pendulum to a vibrating guitar string.
Key Ideas
1Oscillatory Motion. Motion that repeats itself over and over around a central equilibrium (rest) position, such as a mass on a spring or a swinging pendulum.
2Period and Frequency. Period (T) is the time for one complete oscillation; frequency (f) is the number of oscillations per second, related by f = 1/T.
3Amplitude. The maximum displacement from the equilibrium position during an oscillation.
4Restoring Force. A force that always points back toward the equilibrium position, which is what causes and sustains oscillatory motion.
5Damping. The gradual loss of energy (and amplitude) in a real oscillating system, usually due to friction or air resistance, eventually bringing the motion to rest.
Worked Examples
A pendulum completes one full swing every 2 seconds. Find its frequency.
0.5 Hz
A mass on a spring oscillates with frequency 5 Hz. Find its period.
0.2 seconds
Why does a swinging pendulum eventually stop, even though ideal oscillatory motion would continue forever?
Damping (energy loss from friction and air resistance) gradually reduces the amplitude to zero
Formulas
f = 1/T
Practice Yourself
A pendulum swings once every 3s. Find its frequency.
1/3 Hz ≈ 0.33 Hz
An oscillator has frequency 10 Hz. Find its period.
0.1 s
What does 'amplitude' measure?
The maximum displacement from the equilibrium position