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AP® Physics C: Mechanics

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Moderate

Velocity of a Horizontal Mass on a Spring

APPHMC-VIBYT5

A mass is attached to a spring and sits in equilibrium at a position of $x=0$ atop a frictionless table as shown below.

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

The mass is pulled a horizontal distance of $+A$ from its equilibrium position and allowed to oscillate.

Which expression correctly gives the velocity of the mass as a function of time in terms of $m$, $k$, and $A$?

A

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

B

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

C

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

D

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

E

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