A particle's position vector is described by $\vec r = 2\cos \omega t\hat x + 2\sin \omega t\hat y$, where $\omega$ is constant. What is the path of the particle?

A particle is subjected simultaneously to two SHM’s 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

A particle moving along the $x$ axis executes simple harmonic motion, then the force acting on it is given by

A particle is subjected simultaneously to two SHM’s 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

A particle executes $SHM$ with an amplitude of $10\,cm$ and the time period of 1 second. Its average speed during one complete oscillation is

A simple harmonic wave having an amplitude A and time period T is represented by the equation $y = 5{\rm{sin \pi }}\left( {t + 4} \right){\rm{m}}.$ Then the value of A in (metre) and T in (second) are

If the maximum acceleration of a $SHM$ is $\alpha$ and the maximum velocity is $\beta$, then the amplitude of vibration is

The displacement of two identical particle executing SHM are represented by equations {x_1}$$ = \,\,8\,\,\sin $(10\,\,t + \;\;\pi /6\,\,)$ and ${x_2} = 5\,\,\sin \,\,\omega t.$ For what value of ω energy of both the particle is same?

Which of the following combination of Lissajous’ figure will be like eight (8)?

The minimum phase difference between two simple harmonic oscillations, ${y_1} = \frac{1}{2}\sin \,\,\omega t + \frac{{\sqrt 3 }}{2}\cos \,\,\omega t$ ${y_2} = \sin \,\,\omega t + \cos \,\,\omega t,$ is

The displacement of a particle performing simple harmonic motion is given by, $x = 8\,\,\sin \,\,\omega t + 6\cos \omega t,$ where distance is in cm and time is in second. The amplitude of motion is