// multi-utility computation suite · offline · instant · precise
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sci.simple-harmonic-motion Calculator
Calculates simple harmonic motion x(t) = A cos(ωt+φ), velocity, acceleration, and energy E = ½kA² from mass, spring constant, and initial conditions. Period T = 2π/ω = 2π√(m/k) is independent of amplitude — this isochronous property makes SHM the basis of clocks, from pendulums to quartz oscillators.
Inputs
A M
Maximum displacement from equilibrium. Energy carried by a wave is proportional to amplitude squared.
Omega Rad S
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Phi Deg
Reference formula or conversion factor shown for context.
T S
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
displacement x(t) (m)
ISP (specific impulse) — rocket engine efficiency in seconds. Higher ISP means more thrust per kilogram of propellant consumed.
velocity v(t) (m/s)
Reference formula or conversion factor shown for context.
acceleration a(t) (m/s²)
The proportional relationship between two quantities.
period T (s)
Reference formula or conversion factor shown for context.
x = A·cos(ωt + φ)
Reference formula or conversion factor shown for context.