A particle is subjected simultaneously to two SHMs, one along the x -axis and the other along the y -axis. The two vibrations are in phase and have unequal amplitudes. The particle will execute

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TestHub · Accepted Answer

Let the equations of the two mutually perpendicular SHM's of the same frequency and same phase be

$x = a_{1} \sin ω t$ and $y = a_{2} \sin ω t$

Then,

$\frac{y}{x} = \frac{a_{2} \sin ω t}{a_{1} \sin ω t} = \frac{a_{2}}{a_{1}}$

$y = \frac{a_{2}}{a_{1}} x$ , which is the equation of a straight line

Physics - SHM Question with Solution | TestHub

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