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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 angleA1, then forces on this ball are force of stringF[v]andF[g].

F[v1]... component ofF[v]parallel toF[g]and of opposite direction toF[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 angleA, smaller isF[v1]. Why?

I assume it's becauseF[v]is constant no matter what the angleAis, but why is that?

2)

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

I'd imagine angleCode (Text):[B]F[net] = m * g * sin[A1] = m * g * sin[A][/B].

Abeing the same as angleA1only ifF[g] = F[v1]. Then direction ofF[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:

Distance of a ball from equilibrium state can be stated with

, whereCode (Text):

[B]L = A1 * d = A * d [/B]

Lis arc of a circle. When at angleA, the net force on the ball isF = m * g * sin[A], which gives the ball acceleration

Acceleration vectorCode (Text):

[B]a = - g * sin[A][/B]

acertainly isn't linear withL = A * d, and thus the osciliation isn't harmonic. But it becomes harmonic, if angleAis small enough for us to replacesin[A]withA“

a)

I assume by that they mean to say that when arcacertainly isn't linear withL = A * dLis twice as great,aisn't twice as great.

But what has that got to do with harmonic osiclation? Is with harmonic oscillation a linear withL?

Can you show me some proof of that?

b)

First of all, I'm not sure that But it becomes harmonic, if angleA1is small enough for us to replacesin[A1]withA1sin[A1]andA1are ever roughly the same size, since no matter how smallA1is,sin[A1]will always be 100 or more times smaller. Right?

c)

Second, even ifsin[A1]andA1have about the same value whenA1is small enough, what is the purpose of replacingsin[A1]withA1? Why do we want to do that?

d)

Also, why is acceleration vectoranegative?

I realise that whenahas 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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# Homework Help: Urgent: Simple gravity pendulum - don't understand it

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