Questions in Oscillations

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A particle is moving in a circle with uniform speed. Its motion is
Two simple harmonic motions are represented by the equations ${{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)$and ${{y}_{2}}=0.1\cos \pi t.$ The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
Two particles are executing S.H.M. The equation of their motion are ${{y}_{1}}=10\sin \left( \omega \,t+\frac{\pi T}{4} \right),$${{y}_{2}}=25\sin \,\left( \omega \,t+\frac{\sqrt{3}\pi T}{4} \right)$. What is the ratio of their amplitude
The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude
A system exhibiting S.H.M. must possess
If $x=a\sin \left( \omega t+\frac{\pi }{6} \right)$ and ${x}'=a\cos \omega t$, then what is the phase difference between the two waves
A simple pendulum performs simple harmonic motion about $X = 0$ with an amplitude $A$ and time period $T$. The speed of the pendulum at $X=\frac{A}{2}$ will be
A body is executing simple harmonic motion with an angular frequency $2rad/s$. The velocity of the body at $20 mm$ displacement, when the amplitude of motion is $60 mm$, is
A body of mass 5 gm is executing S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/sec. Its velocity will be 50 cm/sec at a distance
A simple harmonic oscillator has a period of 0.01 sec and an amplitude of 0.2 m. The magnitude of the velocity in $m{{\sec }^{-1}}$ at the centre of oscillation is

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