AP® Physics C: Mechanics

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Simple Harmonic Motion: Vertical Springs Differential Equations

APPHMC-X3SEOV

Cinsy Krehbiel. Created for Albert.io. Copyright 2016. All rights reserved.

Three identical, ideal springs and a solid uniform block are configured as shown in the figure above. The mass of the block is $m$ and the spring constant of each spring is $k$.

The block is lifted upward and is then released, causing the block to move up and down in simple harmonic motion.

Which of the following differential equations correctly describes the motion of the system?​

A

$\cfrac { d x }{ dt } =\cfrac{2kx}{m}-g$

B

$\cfrac { { d }^{ 2 }x }{ { dt }^{ 2 } } =\cfrac{2kx}{m}-g$

C

$\cfrac { { d }^{ 2 }x }{ { dt }^{ 2 } } =\cfrac{-2kx}{m}-g$

D

$\cfrac { { d }^{ 2 }x }{ { dt }^{ 2 } } =\cfrac{3kx}{m}-g$

E

$\cfrac { { d }^{ 2 }x }{ { dt }^{ 2 } } =\cfrac{-3kx}{m}-g$