Oscillations Te...

The equation for the displacement of a particle executing SHM is $$y={5 \sin 2 \pi t}$$ cm . Find (i) the velocity at 3cm from the mean position,(ii) acceleration after 0.5s after leaving the mean position.

If the earth loses its atmosphere suddenly, then the duration of day will :-

What of the following quantities are always positive in a SHM

For a particle performing linear S.H.M. its average speed over one oscillation is where $$A$$ is amplitude of S.H.M.

An object of mass $$m$$ is suspended from a spring and it executes $$S.H.M$$ with frequency $$v$$. If the mass is increased $$4$$ times, the new frequency will be:

Choose the correct statements from the following in which k is a real, positive constant:

Two particle execute SHM with same amplitude 'A' and same angular frequency along same line and about same mean position. During oscillation they cross each other in opposite direction at a distance $$\frac{{\sqrt 3 }}{2}A$$ from mean position. The phase difference of two SHM is - 

A heavy bass-sphere is hung from a spiral spring and it executes vertical vibrations with period $$T$$. The ball is now immersed in nonviscous liquid with a density one-tenth that of brass. When set into vertical vibrations with the sphere remaining inside the liquid all the time, the period will be-

A body executes linear simple  harmonic motion of time period $$10 s$$ and amplitude $$2 cm$$. What would be the speed of the body $$2.5 s$$ after it passes through the mean position? 

A pendulum comprising a light string of length $$L$$ and a small sphere, swing in the vertical plane. The string hits a peg located a distance $$d$$ below the point of suspension as shown in figure. If the pendulum is released from the horizontal position ($$\theta = 90^o$$) and is to swing in a complete circle centered on the peg, then the minimum value of $$d$$ is