(Please explain answer!) A block is attached to the end of a horizontal ideal sp

Question

(Please explain answer!) A block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The other end of the spring is attached to a wall. The block is pulled away from the spring’s unstrained position by a distance x0 and given an initial speed of v0 as it is released.

Which one of the following statements concerning the amplitude of the subsequent simple harmonic motion is true?

a) The amplitude will depend on whether the initial velocity of the block is in the +x or the x direction.

b) The amplitude will be less than x0.
c) The amplitude will be equal to x0.
d) The amplitude will be greater than x0.

e) The amplitude will depend on whether the initial position of the block is in the +x or the x direction relative to the unstrained position of the spring.

Explanation / Answer

Balancing energy

1/2M(V0)^2 + 1/2Kx0^2 = 1/2Kx^2

we can clearly see that the x, the resting position or amplitude is always greater than x0

so, option d) The amplitude will be greater than x0.

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