Simple Harmonic...

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

The metallic bob of a simple pendulum has the relative density ρ. The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by

The velocity-time diagram of a harmonic oscillator is shown in the adjoining figure. The frequency of oscillation is

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s² at a distance of 5 m from the mean position. The time period of oscillation is:

A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then its time period of vibration will be:

A particle is executing SHM along a straight line. Its velocities at distances x₁ and x₂ from the mean position are v₁ and v₂, respectively. Its time period is:

The oscillation of a body on a smooth horizontal surface is represented by the equation, X = A cos (ωt) 

where X = displacement at time t 
ω = frequency of oscillation 
Which one of the following graphs shows correctly the variation 'a' with 't'?
Here a = acceleration at time t 
T = time period

Out of the following functions, which represent/s SHM?

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 = a/2 will be:

Which one of the following equations of motion represents simple harmonic motion where k, k₀, k_1, and a are all positive?