AP® Physics C: Mechanics

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Kinetic Energy of a Vertical Mass and Spring System

APPHMC-J2FJBH

A block is hung vertically from a spring attached to the ceiling. It is pulled a distance of $x=+A$ from its equilibrium position and released from rest.

Nick Borowicz. Created for Albert.io, copyright 2016. All rights reserved.

Which of the following expressions correctly gives the kinetic energy $K$ of the block a function of time?

A

$K=|A\cos \left (\sqrt{\cfrac{k}{m}}t \right)|$

B

$K=|\cfrac{1}{2}mA^2 \cos^2 \left (\sqrt{\cfrac{k}{m}}t \right)|$

C

$K=|A\sqrt{\cfrac{k}{m}}\sin \left (\sqrt{\cfrac{k}{m}}t \right)|$

D

$K=|\cfrac{1}{2}kA\sin \left(\sqrt{\cfrac{k}{m}}t\right)|$

E

$K=|\cfrac{1}{2}kA^2\sin^2\left(\sqrt{\cfrac{k}{m}}t\right)|$