A block is attached to an ideal spring. The spring is laid out horizontally alon

Question

A block is attached to an ideal spring. The spring is laid out horizontally along the x-axis, and the block is on a frictionless surface. When the block is at x = 0, the spring is at its natural length. The block is given an initial kinetic energy of 8.00 J, when the block is at x = 0, with the initial velocity directed in the positive x-direction. That kinetic energy is enough to cause the block to move out to x = +d before reversing direction.
(a) How much kinetic energy would the block have to have at x = 0 for the reversal of direction to occur at x = +2d, instead of x = +d?

Explanation / Answer

given K1 = 8 J , x1 =+ d ,x2 =+2d

from conservation of energy
1/2 mv2 = 1/2 kx2

K = 1/2 kx2

K1/K2 = x12 /x22

solving we get

K2 = 32 J

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