01 Key Concepts
Oscillatory 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.
Period 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.
Amplitude
The maximum displacement from the equilibrium position during an oscillation.
Restoring Force
A force that always points back toward the equilibrium position, which is what causes and sustains oscillatory motion.
Damping
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.
02 Key Formulas
- f = 1/T
03 Solved Examples
Example 1 A pendulum completes one full swing every 2 seconds. Find its frequency.
- Apply f = 1/T = 1/2.
Answer: 0.5 Hz
Example 2 A mass on a spring oscillates with frequency 5 Hz. Find its period.
- Apply T = 1/f = 1/5.
Answer: 0.2 seconds
Example 3 Why does a swinging pendulum eventually stop, even though ideal oscillatory motion would continue forever?
- In the real world, air resistance and friction at the pivot remove energy from the system over time.
- This gradual energy loss, called damping, causes the amplitude to shrink until motion stops.
Answer: Damping (energy loss from friction and air resistance) gradually reduces the amplitude to zero
04 Practice Questions
1A pendulum swings once every 3s. Find its frequency.
1/3 Hz ≈ 0.33 Hz
2An oscillator has frequency 10 Hz. Find its period.
0.1 s
3What does 'amplitude' measure?
The maximum displacement from the equilibrium position
4What always causes oscillatory motion to occur?
A restoring force pointing back toward equilibrium
5What causes real oscillations to eventually stop?
Damping (energy loss from friction or air resistance)
📄 Oscillations — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.