Spring oscillations - F = -kx

1. Apr 17, 2012

jsmith613

Looking at the three diagrams we can see that there are three possible situations

(a) mass is to the right of eqm
(b) mass is at eqm
(c) mass is to the left of eqm
(eqm = equilibrium)

Lets look at position (a)

If we consider the tension in both springs:
the tension in the spring on the left has increased by k1x
the tension in the spring on the right has decreased by k2x

So the overall restoring force SHOULD BE k1x - k2x
(the spring on the left is trying to pull it back to the left and the spring on the right is trying to pull it the right hence the forces act in opposite directions)

BUT according to my book the overall restoring force is k1x + k2x....how?

Any help is greatly appreciated

exact quote:

2. Apr 17, 2012

Integral

Staff Emeritus
The compressed spring is not pulling away from the eqm but pushing towards. IE it is under compression.

3. Apr 17, 2012

jsmith613

oh right
thanks

4. Apr 17, 2012

jsmith613

why is tension not present here?
(I don't understand the explanation given)?

Attached Files:

• Tension.png
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5. Apr 17, 2012

Staff: Mentor

I don't understand the choices. There are two forces acting on the hanging mass: gravity and the force from the spring. Of course, a stretched spring exerts a tension. So I don't know the intention of having 'tension' vs 'spring' as separate choices: you could call that force the spring force or the tension force exerted by the spring.

And the given explanation reads like gibberish. Where is this question from?

6. Apr 18, 2012

willem2

Even if both springs are under tension all of the time, the restoring force would still be $k_1x + k_2x$. There's an increased force to the left, because the left spring pulls harder and a decreased force to the right because the right sprint pulls less hard than in the equilibrium position. This will give the same effect as an increased force to the right.

7. Apr 18, 2012

FeX32

A linear spring pulled from equilibrium exerts a force k*x. A linear spring compressed from equilibrium exerts a force k*x. Thus, the force is k*x+k*x.

I'm not sure where the issue lays

8. Apr 18, 2012

FeX32

By the way, that attached .png is garbage, no offence.