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

- Phase Angle Calculator
- Pendulum Calculator (Frequency & Period)
- Conservation of Momentum Calculator (Final Velocity)
- Natural Frequency Calculator
- Damping Force Calculator

## 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?

**First, determine the amplitude.**Measure the amplitude.

**Next, determine the angular frequency.**Measure the angular frequency.

**Next, determine the total time.**Measure the total time of the motion.

**Finally, calculate.**Calculate the displacement, velocity, and acceleration using the formulas above.

## FAQ

**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”