Oscillations Te...

An elastic ball of density $$d$$ is released and it falls through a height $$h$$ before striking the surface of liquid of density $$\rho(d < \rho)$$. The motion of ball is:

The motion of a particle is given by
$$y=4\sin\omega t+8\sin \left(\omega t+\dfrac{\pi}{3}\right)$$
The motion of particle is:

The displacement of a particle in simple harmonic motion in one time period is

There is a clock which gives correct time at $$20^o$$C is subjected to $$40^o$$C. The coefficient of linear expansion of the pendulum is $$12\times 10^{-6}$$ per $$^oC$$, how much is gain or loss in time?

A spring-mass system oscillation in a car. if the car accelerates on a horizontal road, the frequency of oscillation will 

$$m_1$$ and $$m_2$$ are connected with a light inextensible string with $$m_1$$ lying in smooth table and $$m_2$$ hanging as shown in figure. $$m_1$$ is also connected to a light spring which is initially unstretched and the system is released form rest:

A cubical block of side 'a' is floating in a fixed and closed cylindrical container of radius $$2a$$ kept on the ground. Density of the block is $$\rho$$, whereas the density of liquid is $$2\rho$$. Container is made up of conducting wall so that the temperature remains constant. A piston is mounted in the cylinder which can move inside the cylinder without friction. If piston oscillates with large amplitude A.

A hollow sphere is filled with water. It is hung by a long thread to make it a simple pendulum. As the water flows out of a hole at the bottom of the sphere, the frequency of oscillation will

A particle of mass $$m$$ moving along the $$x-$$ axis as a potential energy $$U(x)=a+bx^2$$ where $$a$$ and $$b$$ are positive constants. It will execute simple harmonic motion with a frequency determined by the value of :

A particle executes SHM starting from its mean position at $$t=0$$. If its velocity is $$\sqrt 3 b\omega$$, when it is at a distance $$b$$ from the mean position, when $$\omega==2\pi /T$$, the time taken by the particle to move from $$b$$ to the extreme position on the same side is