List of top Physics Questions on Periodic and oscillatory motions

A test tube of mass 8 g and uniform cross-sectional area 12 cm2 is floating vertically in water. It contains 12 g of lead at the bottom. When the tube is slightly depressed and released, it performs vertical oscillations.
Find the time period of oscillation.

A wheel of angular speed 600 rev/min is made to slow down at a rate of \( 2 \) rad/s\(^2\). The number of revolutions made by the wheel before coming to rest is
A solid cylinder rolls down an inclined plane without slipping. If the translational kinetic energy of the cylinder is 140 J, the total kinetic energy of the cylinder is
Two blocks of masses \( m \) and \( 2m \) are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of 5.4 s is (Acceleration due to gravity = 10 ms\(^{-2}\))
In a spring-block system as shown in the figure, if the spring constant \( K = 9 \, \text{N/m} \), then the time period of oscillation is:
The moments of inertia of a solid cylinder and a hollow cylinder of the same mass and same radius about the axes of the cylinders are \( I_1 \) and \( I_2 \). The relation between \( I_1 \) and \( I_2 \) is
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?
Fig. 13.18 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) 
A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?
Which of the following examples represent periodic motion?