Question

Explain siimple harmonic motion?​

Answer 1

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$


$\bf{SIMPLE\:HARMONIC\:MOTION}$


harmonic oscillation is that oscillation which can be expressed in terms of simple harmonic function sine function cosine function. harmonic oscillation of constant amplitude and of a single frequency is called simple harmonic motion. simple harmonic oscillation is the simplest form of oscillatory motion this motion arises when the force on the oscillating body is directly proportional to its displacement from the mean position.

mathematically SHM can be expressed as see in pic

Answer 2

$simple \: harmonic \: motion$

A particle is said to execute simple harmonic motion if it moves to and fro about a mean position under the action of a restoring force which is directly proportional to its displacement from the mean position and is always directed towards the mean position.

If the displacement of the oscillating body from the mean position is small ;then

$restoring \: force \: \alpha \: displacement \\ \\ f \: \alpha \: x \\ \\ f \: = \: - kx$

This equation defines S.H.M here k is a positive constant called Force constant or spring factor. And is defined as The restoring force produced per unit displacement. The S.I unit of k is Nm^-1

The -ve sign in the above equation shows restoring force F always act in opposite direction of the displacement x.

According to Newton's second Law of motion: -

F = ma

ma =-kx

a= -k/mx

$a \: \alpha \: x$

$examples \: of \: simple \: harmonic \: motion$

✅ Oscillations of a. loaded spring

✅Vibrations of tuning fork

✅Vibrations of the balance wheel of a watch

✅Oscillations of a simple pendulum