Oscillations Te...

A solid cylinder is attached to a horizontal massless spring as shown in figure. If the cylinder rolls without slipping, the time period of oscillation of the cylinder is?

The time taken by a particle performing S.H.M. to pass from point A to B where its velocities are same is $$2$$ seconds. After another $$2$$ seconds, it returns to B. Determine the time period of oscillation is (in seconds).

The spring constants of three springs connected to a mass M are shown in figure. When mass oscillates, what are the effective spring constant and the time period of vibration?

A particle of mass $$m$$ is located in a one dimensional field where potential energy is given by:
$$V(x)=A(1-\cos\ {px})$$ where $$A$$ and $$p$$ are constants.
The period of small oscillations of the particle is

A particle moves with simple harmonic motion in a straight line. In first $$T s$$, after starting from rest it travels a distance $$a$$ and in next $$Ts$$, it travels $$2\ a$$ in same direction, then

A uniform meter stick is suspended through a small pin hole at the 10 cm mark. Find the time period of small oscillation about the point of suspension. 

To and fro motion is an example of 

A light uniform rod of Young's modulus Y, cross sectional area A, coefficient of linear expansion $$\alpha $$ and length $$l_0$$ is rigidly connected to the support at one end and the other end of the rod is connected to the string as shown in the figure. The temperature of the rod is increased by $$\triangle\theta$$ with supports remaining fixed. Initially, the spring is in natural length position. Spring force on the rod acts uniformly over the cross section during elongation of the rod. Find the net of elongation of the rod. (Assume thermal strain to be small) 

A uniform disc of radius R is pivoted at point O on its circumference. The time period of small oscillations about an axis passing through O and perpendicular to plane of disc will be 

An air chamber of volume V has a neck of cross-sectional area a into which a light ball of mass m just fits and can move up and down without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air is B, the time period of the oscillation of the ball is