Simple Harmonic Motion Calculator

Calculate Simple Harmonic Motion





Formulas

The formulas to calculate displacement, velocity, and acceleration in simple harmonic motion are:

\[ y = A \sin(\omega t) \]

\[ v = A \omega \cos(\omega t) \]

\[ a = - A \omega^2 \sin(\omega t) \]

Where:

What is Simple Harmonic Motion?

Simple harmonic motion is defined as the motion of a frictionless pendulum or suspended mass. It describes the oscillatory motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

Example Calculation

Let's assume the following values:

Using the formulas:

\[ y = 5 \sin(2 \times 3) = 5 \sin(6) = -1.41 \]

\[ v = 5 \times 2 \cos(2 \times 3) = 10 \cos(6) = 9.60 \]

\[ a = - 5 \times 2^2 \sin(2 \times 3) = - 20 \sin(6) = 5.64 \]

The displacement is -1.41, the velocity is 9.60, and the acceleration is 5.59.