# A Mass on a Vertical Spring

## Homework Statement

A 1.0 Kg mass is attached to the end of a vertical ideal spring with a force constant of 400 N/m. The mass is set in simple harmonic motion with an amplitude of 10 cm. The speed of the 1.0 kg mass at the equilibrium position is.

A. 2 m/s
B. 4 m/s
C. 20 m/s
D. 40 m/s
E. 200 m/s

EI= EF

## The Attempt at a Solution

I know that at equilibrium the acceleration is zero and that velocity is max.
So using conservation of energy I thought this:
EI= EF
(1/2) k x2 = (1/2) m v2

I have a feeling that this equation does not apply because the spring is vertical
For vertical springs all I know is that the equilibrium position at which the mass simply hangs and does not move.

So at equilibrium the the amount of force required to keep it in equilibrium is
k yeq = mg

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## Answers and Replies

The equation does apply as long as you are referencing x to the equilibrium position.

• Soniteflash
The equation does apply as long as you are referencing x to the equilibrium position.
Ah, Ok that makes sense then.