Homework Help: Urgent: Simple gravity pendulum - don't understand it

1. Dec 4, 2006

kajalove

hi

I know about harmonic oscilation, but I'm having trouble understanding how we derived formulas for gravity pendulum. Please read on.

If a ball on a string ( string is attached to the ceiling ) is displaced from its equilibrium position by angle A1, then forces on this ball are force of string F[v] and F[g].

F[v1] ... component of F[v] parallel to F[g] and of opposite direction to F[g]

http://img473.imageshack.us/img473/1854/nihaloje2.th.png [Broken]

BTW - if picture doesn't show up then please look at the attached jpg file

1)

a)
Now why ( when angle A1 > 0 ) isn't the magnitude of F[v1] equal to F[g] --> F[v1] = -F[g]?

b)
I assume bigger the angle A, smaller is F[v1]. Why?
I assume it's because F[v] is constant no matter what the angle A is, but why is that?

2)
According to my book angles A and A1 are the same:

Code (Text):
[B]F[net] = m * g * sin[A1]  =  m * g * sin[A][/B].

I'd imagine angle A being the same as angle A1 only if F[g] = F[v1]. Then direction of F[net] would be horizontal. But since that is not the case thus the two angles shouldn't be the same.

3)
I will quote my book:

a)
I assume by that they mean to say that when arc L is twice as great, a isn't twice as great.
But what has that got to do with harmonic osiclation? Is with harmonic oscillation a linear with L?
Can you show me some proof of that?

b)
First of all, I'm not sure that sin[A1] and A1 are ever roughly the same size, since no matter how small A1 is, sin[A1] will always be 100 or more times smaller. Right?

c)
Second, even if sin[A1] and A1 have about the same value when A1 is small enough, what is the purpose of replacing sin[A1] with A1? Why do we want to do that?

d)
Also, why is acceleration vector a negative?
I realise that when a has opposite direction to ball's velocity that it has to be negative. But sometimes ball's velocity and acceleration vectors have same direction and thus a should be positive?

cheers

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2. Dec 4, 2006

Hootenanny

Staff Emeritus
Most of your questions can be answered by drawing a free body diagram. For question (a) consider what would happen if Fv1 = -Fg?

3. Dec 4, 2006

kajalove

Ball would start moving in a horizontal direction. I realise that and I know this is not the case, but why doesn't it happen?!

4. Dec 4, 2006

feelau

Um if your angle keeps increasing it eventually reaches 90, so it keeps getting smaller and when it reaches 90 it goes to zero and tension is only determined in x direction since your tension component is basically Tension*cos(theta). I hope that answered the angle part of your problem