# If two mutually perpendicular simple harmonic motion of same amplitude, frequency and having zero phase difference superimpose on a particle then its resultant path will be

Arun
25757 Points
4 years ago

If   $y_{1} = a_{1}\sin\omega t$ and$y_{2} = a_{2}\sin(\omega t + 0) = a_{2}\sin{\omega t}$

$\Rightarrow \frac{y_{1}^{2}}{a_{1}^{2}} + \frac{y_{2}^{2}}{a_{2}^{2}} - \frac{2y_{1}y_{2}}{a_{1}a_{2}} = \Rightarrow y_{2} = \frac{a_{2}}{a_{1}}y_{1}$

This is a equation of straight line.

Resultant equation of two perpendicular SHM when δ = 0 -

Resultant equation

$y= \frac{A_{2}}{A_{1}}.x$

- wherein

It is a straight line with slope

$\frac{A_{2}}{A_{1}}$