# Why does a pendulum overshoot equilibrium

## Homework Statement

"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]

## 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

tiny-tim
Homework Helper
hi jsmith613! "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]

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.

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 … ? 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 … ? 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?

tiny-tim
Homework Helper
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 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 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

tiny-tim
Homework Helper
looks ok (except you might reconsider the word "as" near the end)

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

:) thanks

PhanthomJay