Enter the amplitude, time, angular frequency of an object in simple harmonic motion. The calculator will evaluate and display the velocity, displacement, and acceleration.

Simple Harmonic Motion Formula

The following formulas are used by the calculator above to calculate the displacement, acceleration, and velocity of an object in harmonic motion.

y = A * sin(wt)

v = A * w * cos(wt)

a = - A * w² * sin(wt)

  • Where y is the displacement
  • v is the velocity
  • a is the acceleration
  • w is the angular frequency (rad/sec)
  • t is the time (sec)
  • A is the amplitude

The units for each of the 3 equations above depend on the amplitude. For example, if the amplitude is measure in inches, displacement is in, velocity is in/s, and acceleration is in/s^2

Simple Harmonic Motion Definition

Simple harmonic motion is defined as the motion of a frictionless pendulum or suspended mass.

Simple Harmonic Motion Example

How to calculate simple harmonic motion?

  1. First, determine the amplitude.

    Measure the amplitude.

  2. Next, determine the angular frequency.

    Measure the angular frequency.

  3. Next, determine the total time.

    Measure the total time of the motion.

  4. Finally, calculate.

    Calculate the displacement, velocity, and acceleration using the formulas above.


What is simple harmonic motion?

Simple harmonic motion is motion described by swinging back and forth like a pendulum and taking the assumption that no outside forces act on it. That is it wouldn’t slow down once started. This is obviously a simplistic view since air resistance and friction would work against it, hence the name “simple”