Consider a spring that exerts the following restoring force :
`F = -kx` for `x ge 0`
`F = -4kx` for `x lt 0`
A mass m on a frictionless surface is attached to the spring displaced to `x = A` by strectching the spring and released :

Figure. (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. Figure. (b) shows the same spring with both endsf free and a mass m fixed at each free end Each of the spring is streched by the same force F. The mass in case (a) and the masses in case (b) are then released. Which of the following statements are true?

Figure. (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. Figure. (b) shows the same spring with both endsf free and a mass m fixed at each free end Each of the spring is streched by the same force F. The mass in case (a) and the masses in case (b) are then released. Which of the following statements are true?

The force constant between the restoring force F and displacement x of a spring accoring to the graph shown will be

A slab of mass 'm' is released from a height x to the top a spring of force constant k. The maximum compression of the spring is y. Then

On compressing a spring by 0.5 m, a restoring force of 20 N is developed. When a body of mass 5 kg is placed on the spring, then calculate the (a) force constant of the spring. (b) the distance through which the spring is depressed under the weight of the body. (c ) the period of oscillation of the spring if the the body is pushed down and then released.

In Fig. three identical massless springs are kept horizontal. The left end of the first is tied to a wall. The left end of the second spring is tied to a block of mass m placed on rough ground and the ,eft end of the third spring is tied to a block of mass m placed frictionless ground. The right end of each spring is pulled by a force that is increased gradually from zero to F. Extensions in these springs are x_(1) , x_(2) and x_(3) , respectively. Find the relationship between x_(1) , x_(2) , and x_(3)

In Fig. three identical massless springs are kept horizontal. The left end of the first is tied to a wall. The left end of the second spring is tied to a block of mass m placed on rough ground and the ,eft end of the third spring is tied to a block of mass m placed frictionless ground. The right end of each spring is pulled by a force that is increased gradually from zero to F. Extensions in these springs are x_(1) , x_(2) and x_(3) , respectively. Find the relationship between x_(1) , x_(2) , and x_(3)

In the figure shown the spring is compressed by 'x_(0)' and released . Two block 'A' and 'B' of masses 'm' and '2m' respectively are attached at the ends of the spring. Blocks are kept on a smooth horizontal surface and released. Find the work done by the spring on 'A' by the time compression of the spring reduced to (x_(0))/(2) .

The left and of the spring tied to a wall and at the right end is attached to a block of mass m, which is placed on a frictionless ground. The force F displaces the block by distance x where it is exactly balanced by the spring force. What is the maximum speed of the block in the ensuing motion after the force F is removed?

The left and of the spring tied to a wall and at the right end is attached to a block of mass m, which is placed on a frictionless ground. The force F displaces the block by distance x where it is exactly balanced by the spring force. What is the maximum speed of the block in the ensuing motion after the force F is removed?