## Amplitude of Simple Pendulum

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

You and your friend sit on the same swing and oscillate about the equilibrium position. Your
friend falls off the swing exactly at the highest point (largest amplitude). What will happen to the
amplitude and frequency of your oscillation ?
(a) the amplitude stays the same but the frequency increases
(b) Both amplitude and frequency will stay the same
(c) Amplitude will decrease but frequency stays the same
(d) Only the frequency changes since the mass is now different
(e) Both the amplitude and the frequency will decrease

2. Relevant equations
f=(1/2pi)(√L/g)

3. The attempt at a solution
So I know for sure that the frequency doesn't change with mass so that rules out A, D,and E, but what does the amplitude do with a sudden change in mass? it's not something that usually comes up. My intuition says that the amplitude doesn't change, but im not sure of the maths at this point. im assuming we can take this swing to be a simple pendulum (SH0) for the this problem.

 PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antibacterial clays>> New formula invented for microscope viewing, substitutes for federally controlled drug
 Recognitions: Homework Help What determines the amplitude? Test it out with a home-built pendulum ... though I bet you can imagine one. Since the drop-off point is at maximum displacement, this is the same as catching a model pendulum, pulling one weight, and letting it go again from the same place. You'll find this actually comes up every time a pendulum is set swinging but nobody makes a song and dance about it. Does it make a difference if your friend lets go in mid swing - when speed is a maximum? (he flies off horizontally while you keep swinging) The question has a bit of a fudge but you seem to have nailed the essential - your friend can't just "drop off" - he has to stay where he is while you go on the return spring. Otherwise he'll push on the swing a bit. But you can imagine you are both hanging on to the end of a rope swinging Tarzan style. This also helps because, if your friend is sitting in your lap as described then the center of mass is higher than just with you alone ... and the length of the pendulum is measured to the center of mass - so the frequency does change a bit. I don't think the question wants you to consider that though ;)
 ahh. so ur saying that it's the equivalent (in this idealized case) of me stopping a model pendulum, putting a different weight on, and releasing it from the original max amplitude (angle). so the amplitude wouldn't change in that case.

Recognitions:
Homework Help

## Amplitude of Simple Pendulum

'cause it has already stopped right?
Welcome to PF BTW.

A more fun one is if you set up a Tarzan swing over a river or a lake - give it some nice dimensions like a 5m rope suspected so it is 2m from the water surface when noones swinging on it. Walk the rope-end up a slope by the bank so it is tight and you are 4m vertically from the water surface ... and swing out over the river, and let go to drop in the water: you done this?

The question is - when should you let go to fly the furthest?