(a) What is elastic potential energy of a spring ? Obtain the relation for elastic `P.E. U=(1)/(2)kx^(2)`. Where k is force constant of spring, `x` is extension or compression produced in the spring.

The system is released from rest with both the springs in unstretched positions. Mass of each block is 1 kg and force constant of each spring is 10 N//m . Extension of horizontal spring in equilibrium is

A mass M is suspended as shown in fig. The system is in equilibrium. Assume pulleys to be massless. K is the force constant of the spring. The extension produced in the spring is given by

The spring force is given by F=-kx , here k is a constant and x is the deformation of spring. The F-x graph is

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is:-

Assuming that potential energy of spring is zero when it is stretched by ( x_(0))/( 2) , its potential energy when it is compressed by x_(0) is

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms^(-1) . It collides with a horizontal spring of force constant 200 Nm^(-1) . The maximum compression produced in the spring will be :

A block of mass m rests on a rough horizontal plane having coefficient of kinetic friction mu_(k) and coefficient of static friction mu_(s) . The spring is in its natural, when a constant force of magnitude P=(5mu_(k)mg)/(4) starts acting on the block. The spring force F is a function of extension x as F=kx^(2).( Where k is spring constant ) (a) Comment on the relation between mu_(s) and mu_(k) for the motion to start. (b) Find the maximum extension in the spring ( Assume the force P is sufficient make the block move ) .

A block of 200 g mass is dropped from a height of 2 m on to a spring and compress the spring to a distance of 50 cm. The force constant of the spring is

A block of mass m is suddenly released from the top of a spring of stiffness constant k. a. Find the acceleration of block just after release. b. What is the compression in the spring at equilibrium. c. What is the maximum compression in the spring. d. Find the acceleration of block at maximum compression in the spring.

A force of 10 N holds an ideal spring with a 20 N/m spring constant in compression. The potential energy stored in the spring is