# 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 Calculator:

 INPUT PARAMETERS Known Parameters Mass [m], Spring Constant [k] Frequency [f] Period [T] Angular Frequency [w] Mass [m] g kg oz lb Spring Constant [k] lbf/inch N/mm lbf/ft N/m Frequency  [f] Hz Period [T] s Angular Frequency [w] rad/s Displacement Function Note 2 Sine Function Cosine Function Known Parameters Amplitude [A] or Max. Displacement Max. Velocity Max. Acceleration Displacement at Time t Velocity at Time t Acceleration at Time t Amplitude mm m inch ft Displacement at Time t Max. Positive Velocity mm/s cm/s m/s m/h km/h in/s ft/s mph Velocity at Time t Max. Positive Acceleration mm/s^2 cm/s^2 m/s^2 m/h^2 km/h^2 in/s^2 ft/s^2 miles/h^2 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 $$\varphi$$