# A Mass on a Vertical Spring

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1. Apr 21, 2015

### Soniteflash

1. The problem statement, all variables and given/known data
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

2. Relevant equations
EI= EF

3. 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

Last edited: Apr 21, 2015
2. Apr 21, 2015

### paisiello2

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

3. Apr 21, 2015

### Soniteflash

Ah, Ok that makes sense then.