SIMPLE HARMONIC MOTION CALCULATOR


Simple Harmonic Motion Calculator to find period, frequency, angular frequency, amplitude, displacement, velocity and acceleration of simple harmonic spring oscillator in physics.

The mass of the spring is ignored in calculations. The spring is mounted horizontally and the mass m slides without friction on the horizontal surface. It is also assumed that Hooke's Law holds.


Simple Harmonic Motion Oscillator

Simple Harmonic Motion Calculator:

 INPUT PARAMETERS
Known Parameters
Mass [m]
Spring Constant [k]
Frequency  [f] Hz
Period [T] s
Angular Frequency [w] rad/s
Displacement Function Note 2
Known Parameters
Amplitude
Displacement at Time t
Max. Positive Velocity
Velocity at Time t
Max. Positive Acceleration
Acceleration at Time t
Time t s
Phase Angle Note2 rad

 

Note 1: Use dot "." as decimal separator.

Note 2: Cosine function (X = Acos(wt+φ)) assumes that the oscillating object starts from rest (v = 0) at its maximum displacement (x = A) at t=0 with phase angle 0. If at t = 0 the object is at the equilibrium position and the oscillations are begun by giving the object a push to the positive x direction, it would be a Sine function (X = Asin(wt+φ)) with phase angle 0. See simple harmonic motion example for more information about selection.


RESULTS
Parameter Value
Mass [m] kg
Spring Constant [k] N/mm
Frequency [f]
Hz
Period [T] s
Angular Frequency [w] rad/s
Displacement at 2s mm
Maximum Positive Displacement
Velocity at 2s m/s
Maximum Positive Velocity
Acceleration at 2s m/s^2
Maximum Positive Acceleration




Note: Default rounding is 5 decimal places.

Simple Harmonic Motion Equations:

Angular Frequency $$ w=\sqrt { \frac { k }{ m } } $$
Period $$T=2\pi \sqrt { \frac { m }{ k } } $$
Cosine Function
Position at Function of Time $$x=A\cos { (wt+\varphi ) } $$
Velocity at Function of Time $$\dot { x } =v=-Aw\sin { (wt+\varphi ) } $$
Acceleration at Function of Time $$\ddot { x } =a=-A{ w }^{ 2 }\cos { (wt+\varphi ) } $$
Sine Function
Position at Function of Time $$x=A\sin { (wt+\varphi ) } $$
Velocity at Function of Time $$\dot { x } =v=Aw\cos { (wt+\varphi ) } $$
Acceleration at Function of Time $$\ddot { x } =a=-A{ w }^{ 2 }\sin { (wt+\varphi ) } $$
Spring Constant k
Mass m
Amplitude A
Time t
Frequency f
Phase Angle $$\varphi $$


Reference: