Simple Pendulum Amplitude and Frequency Changes Due to Mass Variation

[fizz-eek!]

Homework Statement

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

Homework Equations

f=(1/2pi)(√L/g)

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 I am not sure of the maths at this point. I am assuming we can take this swing to be a simple pendulum (SH0) for the this problem.

 

[Simon Bridge]

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 let's 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 ;)

 

[fizz-eek!]

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.

 

[Simon Bridge]

'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?
(State your assumptions.)

 

[fizz-eek!]

at max amplitude, the rope would come to a fleeting halt (same thing as in the swing problem). so i think that to fly furthest you'd have to let go right at the bottom of the swing where KE is max, if u let go at the top, u'd just drop, you only have potential energy at that point.

 

[Simon Bridge]

Ahhh... but prove it?
And what were your assumptions?

If you let go at the bottom, you'd have only 2m to drop before splash - even though you'd have max horizontal speed. Let go a bit later, then your velocity has an upwards component, giving you some loft, as well as being higher so there's further to fall. OTOH: you've lost some speed ... but maybe the angle and height make up for it?

Also you need to consider if it is furthest since letting go that is important or furthest across the river? I didn't specify ;) Perhaps the rope will carry you further than you can fly?

Both are doable at your level - just a bit more involved than you are used to.
Energy arguments are the right way to go.

See what I mean though - this sort of puzzle is intrinsically interesting.

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aside: you'll notice that hardly anyone uses txt-style abbreviation in the serious forums. you know, writing "u" instead of "you" and that?
Part of the reason is that we often want to use single letters as variables and it can be confusing and partly because it just makes us look illiterate when we are trying to look smart. You're not doing it a lot, but it is worth thinking about.