The equations of two waves acting in perpendicular directions are given as $x=a \cos (\omega t+\delta)$ and $y=a \cos (\omega t+\alpha)$,where $\delta=\alpha+\frac{\pi}{2}$. The resultant wave represents:

$A$ particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by $x = a_1 \cos \omega t$ and $y = a_2 \cos 2 \omega t$ traces a curve given by:

Two particles undergo $SHM$ along parallel lines with the same time period $(T)$ and equal amplitudes $(A)$. At a particular instant,one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time:

The composition of two simple harmonic motions of equal periods at right angles to each other and with a phase difference of $\pi$ results in the displacement of the particle along

The equation of $SHM$ is given as:
$x = 3 \sin(20\pi t) + 4 \cos(20\pi t)$,
where $x$ is in $cm$ and $t$ is in $seconds$. The amplitude is ..... $cm$.

Two $SHM$ are represented by equations,$y_1 = 6\cos \left( {6\pi t + \frac{\pi }{6}} \right)$ and $y_2 = 3\left( {\sqrt 3 \sin 3\pi t + \cos 3\pi t} \right)$. Which of the following statements is true?