Simple Harmonic Motion: Definition, Equation, Diagram & Real-Life Examples
Master Simple Harmonic Motion (SHM) — the most important type of periodic motion. Learn the SHM equation, displacement graph, restoring force, and see real examples like pendulums and springs.
What is Simple Harmonic Motion?
Simple Harmonic Motion (SHM) is a special type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts towards it.
It is the purest form of oscillatory motion and forms the foundation for understanding waves, sound, and many systems in physics.
Key Features of SHM
- Restoring Force: F = -kx (Hooke’s Law)
- Acceleration: Directly proportional to displacement and opposite in direction
- Period & Frequency: Independent of amplitude (for small oscillations)
- Energy: Continuously converts between kinetic and potential energy
SHM Equation
x = A sin(ωt + φ)
Where:
x = displacement
A = amplitude
ω = angular frequency (ω = 2πf)
φ = phase constant
Displacement-Time Graph of SHM
The motion is sinusoidal. The object oscillates between +A and -A with constant period T.
Real-Life Examples of Simple Harmonic Motion
Simple Pendulum
For small angles, a swinging pendulum shows nearly perfect SHM. Period depends only on length.
Mass on a Spring
When stretched or compressed, the mass oscillates with SHM according to Hooke’s Law.
Guitar / Violin Strings
Vibrating strings produce sound through simple harmonic motion.
Heart Beat & Breathing
Many biological rhythms approximate SHM for small amplitudes.
Important Formulas for SHM
Period (T) = 2π √(m/k)
For mass-spring system
Period (T) = 2π √(L/g)
For simple pendulum (small angles)
Angular frequency ω = 2πf = √(k/m)
Maximum velocity = ωA
Occurs at equilibrium position
Solved Practice Problems
Problem 1: A mass of 0.5 kg is attached to a spring with spring constant 200 N/m. Calculate the period of oscillation.
T = 2π √(m/k) = 2π √(0.5/200) ≈ 0.314 seconds
Problem 2: A simple pendulum has length 1 m. What is its time period on Earth? (g = 9.8 m/s²)
T = 2π √(L/g) ≈ 2.01 seconds
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