Simple Harmonic Motion
2.0 Causes of Oscillation
2.0 Causes of Oscillation
Consider a particle which is free to move on a horizontal axis ($x$ – axis) is acted upon by a force given as: $$F = - k{x^n}$$ where
$k$ = is a positive constant.
$x$ = displacement from fixed point O.
$F$ = Force.
Now, the following cases are possible depending on the value of $n$.
- When ‘$n$’ is an even integer ($0,\ 2,\ 4,…..$ etc), force will always act along the negative $x$ – axis, whether ‘$x$’ is positive or negative. Therefore the motion of the particle in non oscillatory.
- When ‘$n$’ is an odd integer ($1,\ 3,\ 5,….$ etc), force will act along negative $x$ – axis for $x > 0$, and force will act along positive $x$ – axis for $x < 0$. Thus the particle performs oscillatory motion about the stable equilibrium position ($x = 0$).
- For, $n = 1$, $F=-kx^{n}$, the equation of motion is said to be SHM (Simple Harmonic Motion).
