# Simple Harmonic Motion Calculator

A kind of periodic motion in which the restoring force acting is directly proportional to the displacement and acts in the opposite direction to that of displacement is called as simple harmonic motion. The important factors associated with this oscillatory motion are the amplitude and frequency of the motion. Use the simple harmonic motion calculator to calculate the angular frequency, velocity, and acceleration known the input values frequency, displacement and time.

A kind of periodic motion in which the restoring force acting is directly proportional to the displacement and acts in the opposite direction to that of displacement is called as simple harmonic motion. The important factors associated with this oscillatory motion are the amplitude and frequency of the motion. Use the simple harmonic motion calculator to calculate the angular frequency, velocity, and acceleration known the input values frequency, displacement and time.

Code to add this calci to your website

#### Formula:

ω = 2πf
v = Aω cos (ωt)
a= - d ω^{2} sin (ωt)
**Where,**
ω = Angular Frequency
f = Frequency
v = Velocity
A = Ampltude
t = Time
d = Displacement
a = Acceleration

#### Example

**
Solve for acceleration, velocity and angular frequency using simple harmonic equations.**
Given :

Frequency = 10 Hz

Displacement = 8 mm

Time = 5 seconds

Solution:

ω = 2x3.14 x 10

= 62.8319 rad/s

v = A x 62.8319 cos (62.8319 x 5)

= 502.6548

a= -[ 8 x 62.8319 ^{2} sin (62.8319 x 5)]

= 31582.7341 mm/s^2