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Calcimator

Simple Harmonic Motion Calculator

Displacement, velocity, and acceleration at any time in SHM.

Inputs

Results

Displacement (m)

0

Velocity (m/s)

-0.31

Acceleration (m/s²)-0
Frequency (Hz)0.5
Angular Frequency (rad/s)3.14
Max Velocity (m/s)0.31
Max Acceleration (m/s²)0.99
Kinetic Energy0.05
Potential Energy0
Total Energy0.05
How to Use This Calculator
  1. Enter amplitude (m) — the maximum displacement from equilibrium.
  2. Enter period (s) — the time for one complete oscillation.
  3. Enter time (s) at which to evaluate the motion and the phase constant (rad).
  4. Read displacement (m) and velocity (m/s) at the specified time.
  5. Review angular frequency (rad/s), maximum velocity (m/s), and maximum acceleration (m/s2).

What each input means

Amplitude (m)
Maximum displacement from equilibrium.
Period (s)
Time for one complete oscillation.
Time (s)
Time at which to evaluate position/velocity/acceleration.
Phase Constant (rad)
Initial phase offset in radians.

What each result means

Displacement (m)
x(t) = A·cos(ωt + φ).
Velocity (m/s)
v(t) = -Aω·sin(ωt + φ).
Acceleration (m/s²)
a(t) = -Aω²·cos(ωt + φ).
Frequency (Hz)
f = 1/T.
Angular Frequency (rad/s)
ω = 2π/T.
Max Velocity (m/s)
v_max = Aω at equilibrium.
Max Acceleration (m/s²)
a_max = Aω² at endpoints.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Amplitude (m) = 0.1, Period (s) = 2, Time (s) = 0.5, Phase Constant (rad) = 0 = 4 input(s) provided
  2. Calculate Displacement
    0 = 0
  3. Calculate Velocity
    -0.31416 = -0.31416
  4. Calculate Acceleration
    0 = 0
  5. Calculate Frequency
    Frequency = 1 / periodS
    0.5 = 0.5

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