Simple Harmonic Motion Calculator

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Kinematic mode uses frequency directly. Spring-mass mode derives frequency from the spring constant and mass.
Number of complete oscillations per second. Ignored in spring-mass mode (computed from k and m).
Hz
Maximum displacement from the equilibrium position, in metres.
m
Elapsed time from t = 0 at which to evaluate displacement, velocity, and acceleration.
s
Initial phase offset in radians. Use 0 for a sine start (zero displacement at t = 0). Use pi/2 (1.5708) for a cosine start (maximum displacement at t = 0).
rad
Displacement (y)
0.1m

y = A * sin(omega * t + phi)

Angular frequency (omega)6.2832rad/s
Period (T)1s
Velocity (v)0m/s
Acceleration (a)-3.9478m/s²
Max velocity (v_max)0.6283m/s
Max acceleration (a_max)3.9478m/s²
Displacement (m)0.1
Velocity (m/s)0

Displacement is 0.100000 m, velocity is 0.0000 m/s.

  • At this moment the object is at 100.0% of its maximum displacement (0.1 m from equilibrium).
  • The restoring acceleration is 3.9478 m/s^2, directed toward the equilibrium position.
  • One complete oscillation takes 1.0000 s. The angular frequency is 6.2832 rad/s.

Next stepThe object is near its turning point: velocity approaches zero and acceleration (restoring force) is at its maximum.

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