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Vertical Motion of a Mass on a Spring

APPHMC-2LJQLR

TOMIHIRO ONO. Created for Albert.io. Copyright 2016. All rights reserved.

A mass $m$ hung on a vertical ideal spring (of spring constant $k$) is initially held at its highest position above equilibrium such that the spring is compressed by $x_1$. When released, the mass falls through a distance $2h$ such that the lowest point it reaches is when the spring is stretched by $x_2$.

Based on this, what is $x_2 - x_1$? Neglect energy loss through friction or air resistance.

A

$0$

B

$h$

C

$2h$

D

$\cfrac {mg} k$

E

$\cfrac {2mg} k$