Explain briefly about oscillations.

One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the liquid column of mercury in the U-tube executes simple harmonic motion.

Consider a simple pendulum having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple. Pendulum depends on its length (I), mass of the bob, (m) and acceleration due to gravity (g). Derive the expression for its time period using method of dimension.

Two simple harmonic moles are represented by Y₁=0.1 sin (100 \(\pi\)t + \(\pi\)/3) and Y₂=0.1 cos what is the phase difference of the velocity of the particle 1 with respect to the velocity of particle?

A simple pendulum has time period T, the point of suspension is now moved upward acceleration to the relation Y= kt² (k = 1 ms^-2) where Y is the verticle displacement the time period now becomes T₂. What is the ratio \(\frac { { T }_{ 1 }^{ 2 } }{ { T }_{ 2 }^{ 2 } } \)? Given g=10 ms^-2.