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.
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.
|
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 |
$$\varphi $$ |