Simple Harmonic Motion Calculator

Amplitude (A in meters):

Angular Frequency (ω in rad/s):

Initial Phase (φ in degrees):

Time (t in seconds):

Mass (m in kg):

Results

Understanding Simple Harmonic Motion

What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to displacement from equilibrium. Examples include springs and pendulums.

Displacement follows sinusoidal pattern
Force is proportional to displacement
Energy oscillates between kinetic and potential
Period is independent of amplitude

Key Equations

Motion Equations:

x(t) = A·cos(ωt + φ)

v(t) = -Aω·sin(ωt + φ)

a(t) = -Aω²·cos(ωt + φ)

Energy Equations:

KE = ½mv²

PE = ½kx²

Total Energy = ½kA²

Applications

Physics

Spring systems
Pendulum motion
Sound waves

Engineering

Vibration analysis
Seismic studies
Mechanical systems