Oscillations Te...

A clock which has pendulum made of brass keeps correct time at $$30^\circ {\text{C}}$$. How many seconds it will lose or gain in a day if temperature falls to $$0^\circ {\text{C}}$$. $$\left( {\alpha _{brass}  = 1.8 \times 10^{ - 3} /^\circ {\text{C}}^{ - 1} } \right)$$

Calculate the period of oscillations of block of mass m attached with a set of springs as shown

A thin spherical shell of mass $$M$$ and radius $$R$$ has a small hole. A particle of mass $$m$$ is released at its mouth. Then

The string of a pendulum is horizontal initially. The mass of the bob attached is m. Now the string is released. 'R' is the length of the pendulum.
(i) Velocity of the string at an angle $$30^\circ$$ with the vertical is ________

The bob of a simple pendulum is displaced from its equilibrium position O to a position Q which is at height h above O and the bob is then released. Assuming the mass of the bob to be m and time period of oscillations to be 2.0 sec, the tension in the string when the bob passes through O is :

A bob of a stationary pendulum is given a sharp hit to impart it  a horizontal speed of $$\sqrt{3 gl}.$$ Find the angle rotated by the string before it becomes slack.

The velocity of a particle under going SHM at the mean position is $$2{ms}^{-1}$$. The velocity of the particle at the point where the displacement from the mean position is equal to half the amplitude is

A particle of mass $$0.2\ kg$$ is executing $$SHM$$. The velocity displacement curve for which is shown in figure. The frequency of oscillation is:

A body of mass $$m$$ has time period $$T_1$$ with one spring and has time period $$T_2$$ with another spring. if both the spring are connected in parallel and same mass is used, then new time period $$T$$ is given as

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?