Questions in Oscillations

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The phase of a particle executing simple harmonic motion is $\frac{\pi }{2}$ when it has
A particle starts S.H.M. from the mean position. Its amplitude is $A$ and time period is $T$. At the time when its speed is half of the maximum speed, its displacement y is
The amplitude and the periodic time of a S.H.M. are 5cm and 6sec respectively. At a distance of 2.5cm away from the mean position, the phase will be
Two equations of two S.H.M. are $y=a\sin \,(\omega \,t-\alpha )$ and $y=b\cos (\omega \,t-\alpha )$. The phase difference between the two is
The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 sec respectively. If the initial phase is $\pi /2$ radian, then the equation of S.H.M. will be
The equation of S.H.M. is $y=a\sin (2\pi nt+\alpha )$, then its phase at time t is
A particle is oscillating according to the equation$X=7\cos 0.5\pi t$, where $t$ is in second. The point moves from the position of equilibrium to maximum displacement in time
A simple harmonic oscillator has an amplitude a and time period T. The time required by it to travel from x = a to x = a / 2 is
Which of the following expressions represent simple harmonic motion
A $1.00\times {{10}^{-20}}kg$ particle is vibrating with simple harmonic motion with a period of $1.00\times {{10}^{-5}}sec$ and a maximum speed of $1.00\times {{10}^{3}}m/s$. The maximum displacement of the particle is

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