  # Displacement function in SHM

Physics

## example

### Extreme Position(Amplitude) of a particle performing SHM

Example : A particle moves along y-axis according to the equation y (in cm).Find whether the motion is simple harmonic or not.Also, calculate amplitude of particle and its mean position.
Solution:
The given equation can be written as

or

Mean position cm

## example

### Use phase to understand relative position between two SHMs

Example: What is the minimum phase difference between two SHMs  ?

Solution:

Thus phase difference is

## shortcut

### Find time taken to travel between two given positions in SHM

Example: A particle executes SHM along a straight line with mean position at and with a period of sec and amplitude of cm. Find the shortest time taken by it to go from cm to cm ?

Solution:
sin( )

let at , thus
sin

Now for at , let , thus we have

or

Solving we get

## law

### Displacement as a function of time is a simple harmonic motion

Standard equation of simple harmonic motion is:

Any general equation satisfying the above criterion represents a simple harmonic motion.
i.e.

## formula

### Angular displacement as a function of time

In angular SHM equation of motion is given by:

General equation for angular displacement:

## diagram

### Shift of displacement-time plot with change in phase

In the given plot, phase difference is