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kajalove

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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

http://img473.imageshack.us/img473/1854/nihaloje2.th.png

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

a)

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

b)

I assume bigger the angle

I assume it's because

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

I'd imagine angle

I will quote my book:

a)

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

Can you show me some proof of that?

b)

c)

Second, even if

d)

Also, why is acceleration vector

I realize that when

cheers

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

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:

`[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:

Distance of a ball from equilibrium state can be stated with

, whereCode:`[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

Code:`[B]a = - g * sin[A][/B]`

Acceleration vectoracertainly 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 * d

**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 thatBut it becomes harmonic, if angleA1is small enough for us to replacesin[A1]withA1

**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 realize 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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