Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at `0 = 45°` with the horizontal. Assuming that the inclined plane is frictionless. Assuming that the time period of oscillation of the simple pendulum is T. Find the value of T.

A simple pendulum of length l is suspended from the ceilling of a car moving with a speed v on a circular horizontal road of radius r. a. Find the tension in the string when it is at rest with respect to the car. b.Find the time period of small oscillation.

The pulley shown in figure has a radius 10 cm and moment of inertia 0.5 kg-m^2 about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4.0 kg block.

Find the period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination alpha .

A simple pendulum of length 40 cm oscillates with an angular amplitude of 0.04 rad. Find a. the time period b. the linear amplitude of the bob.

A metallic rod of linear density is 0.25 kg m^(-1) is lylong horizontally on a smooth inclined plane which makes an angle of 45^(@) with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of strength 0.25 T is acting on it in the vertical direction. Calculates the electric current flowing in the rod to keep it stationary .

A simple pendulum is suspended from the ceiling a car accelerating uniformly on a horizontal road. If the acceleration is a_0 and the length of the pendulum is l, find the time period of small oscillations about the mean position.