📐 SHM Formulas
x(t) = A × cos(ωt + φ)
v(t) = -Aω × sin(ωt + φ)
a(t) = -Aω² × cos(ωt + φ)
ω = 2πf = 2π/T
v_max = Aω
a_max = Aω²
E = ½mω²A²
Where:
A = Amplitude
ω = Angular frequency
f = Frequency
T = Period
φ = Initial phase
m = Mass
Understanding Simple Harmonic Motion
Simple Harmonic Motion (SHM) is a fundamental concept in physics describing oscillatory motion where the restoring force is proportional to displacement. This simple harmonic motion calculator helps analyze all key parameters.
Key Parameters
- Amplitude (A): Maximum displacement from equilibrium
- Period (T): Time for one complete oscillation
- Frequency (f): Oscillations per second (Hz)
- Angular Frequency (ω): Rate of phase change (rad/s)
Examples of SHM
- Pendulum clocks (small angles)
- Mass-spring systems
- Vibrating strings
- Molecular vibrations
- LC electrical circuits
Frequently Asked Questions
What is simple harmonic motion?
Simple harmonic motion is oscillatory motion where the restoring force is directly proportional to displacement. Common examples include pendulums and mass-spring systems.
How do I calculate the period of SHM?
Period T = 2π/ω = 1/f. For a mass-spring system: T = 2π√(m/k). For a pendulum: T = 2π√(L/g).
When is velocity maximum in SHM?
Velocity is maximum when passing through equilibrium (x = 0). Maximum velocity v_max = Aω.
When is acceleration maximum?
Acceleration is maximum at extreme positions (x = ±A). Maximum acceleration a_max = Aω².
Is this calculator free?
Yes! This simple harmonic motion calculator is completely free for students and educators.