What is Simple Harmonic Motion?
Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. Think of a mass on a spring or a swinging pendulum.
🔧 Spring-Mass System
A mass attached to a spring oscillates back and forth.
🕰️ Simple Pendulum
A mass swinging at the end of a string.
Key Concepts
Period (T) and Frequency (f)
The period is the time for one complete oscillation. The frequency is how many oscillations per second.
T = 1/f
f = 1/T (measured in Hz)
Angular Frequency (ω)
The rate at which the phase changes, measured in radians per second.
ω = 2πf = 2π/T
Amplitude (A)
The maximum displacement from equilibrium. Important: for small angles, the period of a pendulum is independent of amplitude.
Essential Formulas
Spring-Mass System
T = 2π√(m/k)
ω = √(k/m)
T increases with mass, decreases with stiffer springs
Simple Pendulum (small θ)
T = 2π√(L/g)
ω = √(g/L)
Period depends only on length and gravity, not mass!
Position and Velocity
x(t) = A·cos(ωt)
v(t) = -Aω·sin(ωt)
vₘₐₓ = Aω
Energy in SHM
In undamped SHM, total mechanical energy is conserved. Energy continuously converts between kinetic and potential forms.
Potential Energy
PE = ½kx²
Max at extremes
Kinetic Energy
KE = ½mv²
Max at equilibrium
Total Energy
E = ½kA²
Constant
Ready to Practice?
Test your understanding with randomized oscillation problems.
Start Practicing →Interactive Demo
Experiment with spring-mass and pendulum systems. Observe how changing mass, spring constant, or length affects the period.