Oscillations Te...

For a simple pendulum, relation between time period $$T$$, length of pendulum $$l$$ and acceleration due to gravity $$g$$ is given by : 

When a simple pendulum is taken from the Equator to the Pole, its period of oscillation will :

A tunnel is dug along the diameter of the earth. A mass $$m$$ is dropped into it. How much time does it take to cross the earth?

One end of a rod of length L is fixed to a point on the circumference of a wheel of radius R. The other end is sliding freely along a straight channel passing through the centre O of the wheel as shown in the figure. The wheel is rotating with a constant angular velocity $$\omega$$ about O. Taking $$\displaystyle T=\frac{2\pi}{P\omega}$$ the motion of the rod is?

A mass $$m$$ is suspended from the two coiled spring which have the same length in unstreched condition. Two springs are connected in parallel.  The force constant for springs are $$K_{1}$$ and $$K_{2}$$. The time period of the suspended mass will be

The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $${E}_{1}$$ and $${E}_{2}$$ are the total mechanical energies respectively. Then

A simple harmonic motion has an amplitude $$A$$ and time period $$T$$. The time required by it to travel $$x = A$$ to $$x = \dfrac {A}{2}$$ is:

A spring has a certain mass suspended from it and its period for vertical oscillation is $$T$$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

When the cylinder is slightly depressed and released,it oscillates.Let there be a mean position.Find time period

A particle performs S.H.M of amplitude $$A$$ along a straight line. When it is at distance $$\cfrac { \sqrt { 3 }  }{ 2 } A$$ from mean position, its kinetic energy gets increased by an amount $$\cfrac { 1 }{ 2 } m{ \omega  }^{ 2 }{ A }^{ 2 }$$ due to an impulsive force. Then its new amplitude becomes