A load of mass M is on horizontal rails. A pendulum made of a ball of mass m tied to a weightless inextensible thread is suspended to the load. The load can move only along the rails. Determine the ratio of the periods `T_(2)//T_(1)` of small oscillations of the pendulum in vertical planes parallel and perpendicular to the rails.

A block of mass M rests on a smooth horizontal table. There is a small gap in the table under the block through which a pendulum has been attached to the block. The bob of the simple pendulum has mass m and length of the pendulum is L. The pendulum is set into small oscillations in the vertical plane of the figure. Calculate its time period. The table does not interfere with the motion of the string.

Two blocks having mass m and 2m and connected by a spring of rigidity k lie on a horizontal plane. Determine the period T of small longitudinal oscillations of the ystem, neglecting friction.

A wagon of mass M can move without friction along horizontal rails. A simple pendulum consisting of a sphere of mass m is suspended from the ceiling of the wagon by a string of length l. At the initial moment the wagon and the pendulum are at rest and the string is deflected through an angle alpha from the vertical. Find the velocity of the wagon when the pendulum passes through its mean position.

A weightless rigid rod with a load at the end is hinged at point A to the wall so that it can rotate in all directions (Fig). The rod is kept in the horizontal position by a vertical inextensible thread of length 1, fixed at its midpoint. The load receives a momentum in the direction perpendicular to the plane of the figure. Determine the period T of small oscillations of the system.

Two loads of the same mass are tied to the ends of a weightless inextensible thread passed through a weightless pulley (Fig. ). Initially, the system is at rest,and the loads are at the same level. Then the right load abruptly acquires a horizontal velocity v in the plane of the figure. Which load will be lower in a time?

A flat spiral spring of force constant K is loaded with mass M and oscillates vertically with a time period T. Then the mass suspended to the free end is

A pendulum consisting of a small sphere of mass m, suspended by a inextensible and massless string of length 1 , is made to swing in a verticle plane. If the breaking strength of the string is 2 mg, then the maximum angular amplitude of the displacement from the verticle can be

A simple pendulum of length 1 m is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of 2m//s^2 is (use g=10 m//s^2 )

A flat spiral spring of force constant k is loaded with mass M and oscillate about vertical with a time period T. Then the mass suspended to the free end is

A small bob attached to a light inextensible thread of length l has a periodic time T when allowed to vibrate as a simple pendulum. The thread is now suspended from a fixed end O of a vertical rigid rod of length (3l)/(4) (as in figure). If now the pendulum performs periodic oscillations in this arrangement, the periodic time will be-