# Why does a pendulum overshoot equilibrium

1. May 16, 2012

### jsmith613

1. The problem statement, all variables and given/known data
"A pendulum is released from a height of h metres. At the equilibrium point the resultant force on the pendulum is zero. Explain why the pendulum continues to oscillate in spite of this" [3 marks]

2. Relevant equations

3. The attempt at a solution

So I presume that it had something to do with the inertia of the pendulum (i.e: newtons first law). But I don't know how to correctly phrase the 3-mark answer. Could someone please help.

Thanks

2. May 16, 2012

### tiny-tim

hi jsmith613!
well, there's at least 1 mark for actually writing out newton's first law!

then i suppose 1 mark for applying it to the particular case …

and maybe 1 mark for doing it in tolerable english

also, since the question says "oscillate", which means going backward and forward, you'd better say something about that too

btw, is this an ordinary swinging pendulum?

if so, the question is wrong, the resultant force is non-zero since it has to equal … ?

3. May 16, 2012

### jsmith613

Newton's First law states that a body will remain in a state of uniform motion unless an external resultant force acts. At all times, the resultant force acts towards the equilibrium position. As the pendulum approaches this position, it accelerates towards the equlibrium position so it speeds up. At equilibrium EXACTLY no force acts on the pendulum BUT the body still has inertia so continues to move.
At maximum amplitude the body has zero inertia but maximum acceleration. This causes the body to move back to equilibrium and hence oscillate

Do you think this would get 3 marks?

4. May 16, 2012

### tiny-tim

personally, i hate the word "inertia", i use momentum (or velocity as appropriate)

but if your professor uses it, then you'd better copy him!​

apart from that, it looks ok

5. May 16, 2012

### jsmith613

ok how is this:

Newton's First law states that a body will remain in a state of uniform motion unless an external resultant force acts.
At all times, the resultant force acts towards the equilibrium position. As the pendulum approaches this position, it accelerates towards the equlibrium position so it speeds up.

At equilibrium EXACTLY no force acts on the pendulum BUT the body still has momentum (which is conserved if not external forces act on the system, as at equilibrium) so continues to move.

At maximum amplitude the body has no momentum as the restoring force is acting to reduce the momentumof the body but the body has maximum acceleration. This causes the body to move back to equilibrium and hence oscillate

6. May 16, 2012

### tiny-tim

looks ok

(except you might reconsider the word "as" near the end)

7. May 16, 2012

### jsmith613

:) thanks

8. May 16, 2012

### PhanthomJay

What still needs to be resolved , however, is that is not correct to say that the pendulum is in equilibrium at the bottom of the swing, since it is being acted on by a net centripetal force. The forces acting on it in the vertical direction are non zero . Once released, it is never in equilibrium until a damping force or other externally applied force brings it to a halt.