# Spring and force problem

1. Feb 17, 2013

### daveyboy157

1. The problem statement, all variables and given/known data
Suppose a 1 kg mass hangs from a spring with rest length of 2 m and spring constant of 100 N/m. Then, the spring is compressed by 0.5 m. Using up as the positive direction and ignoring drag, give the following with units:

(a) The weight displacement
(b) The equilibrium position
(c) The maximum length
(d) The sign of the initial restoring force
(e) The restoring force when the length of the spring is 3.15 m

2. Relevant equations
Fs = -kx
F = ma

3. The attempt at a solution
a) .5
b)This is what i do not know
c)also do not know
d)Fs = Force of spring
e)Fs = 100N/m *3.15m -> 315N

2. Feb 17, 2013

### Staff: Mentor

b) Can you calculate the weight extending the spring? How is this related to the extension of the spring (at equilibrium) and the spring constant?
c) Quickest way: the oscillation will be symmetric around the equilibrium position.
d) The answer is a sign (+ or -).
e) Test your answer with the restoring force at a length of 2m. What do you expect?

3. Feb 17, 2013

### daveyboy157

a) .5m displacement is stretched - un-stretched
b) I am really confused here, I do not know how to calculate weight of extended spring. Also, where is the equilibrium, at rest length or un-stretched length?

c) How do i see the oscillation of this spring?

4. Feb 17, 2013

### haruspex

The equilibrium position is the one where it would remain stationary if set stationary. I.e., all the forces balance. This will not be the unstretched position, because some stretch is needed to balance the force of gravity. Neither will it be the instantaneous rest position of the oscillation.