# Understanding Simple Gravity Pendulum - Urgent Help Needed

• kajalove
In summary: For question (b), I assume that the larger the angle A, the smaller the magnitude of F[v1]. Why is that? Think about it this way. The more angles A there are, the greater the number of vectors F[v1]. Each vector has a magnitude and direction, and the more vectors there are, the greater the magnitude and direction of each vector. So the more angles there are, the smaller the magnitude of F[v1] will be. For question (c), I assume that the acceleration vector a is not linear with the distance L. Why is that? Think about it this way. If the acceleration vector a was linear with distance L, then the o
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

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

Code:
[B]L = A1 * d = A * d [/B]
, where L is arc of a circle. When at angle A, the net force on the ball is F = m * g * sin[A], which gives the ball acceleration
Code:
[B]a = - g * sin[A][/B]

Acceleration vector a certainly isn't linear with L = A * d, and thus the osciliation isn't harmonic. But it becomes harmonic, if angle A is small enough for us to replace sin[A] with A

a)
a certainly isn't linear with L = A * d
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)
But it becomes harmonic, if angle A1 is small enough for us to replace sin[A1] with A1
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 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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Most of your questions can be answered by drawing a free body diagram. For question (a) consider what would happen if Fv1 = -Fg?

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

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

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

## 1. What is a simple gravity pendulum?

A simple gravity pendulum is a weight (called a bob) attached to a string or rod that is able to swing freely from a fixed point. It is often used as a model to understand the behavior of more complex pendulum systems.

## 2. How does a simple gravity pendulum work?

A simple gravity pendulum works by utilizing the force of gravity to create a back-and-forth swinging motion. As the bob is released from a certain height, it will swing back and forth in a predictable pattern until it comes to rest due to friction and air resistance.

## 3. What factors affect the period of a simple gravity pendulum?

The period (or time it takes for one swing) of a simple gravity pendulum is affected by three factors: the length of the string, the mass of the bob, and the strength of gravity. A longer string, larger mass, and stronger gravity will all result in a longer period.

## 4. How can I calculate the period of a simple gravity pendulum?

The period of a simple gravity pendulum can be calculated using the equation T = 2π√(L/g), where T is the period in seconds, L is the length of the string in meters, and g is the acceleration due to gravity (9.8 m/s² on Earth).

## 5. What are some real-world applications of the simple gravity pendulum?

The simple gravity pendulum has many real-world applications, including timekeeping devices (such as grandfather clocks), seismometers for measuring earthquakes, and amusement park rides. It is also used in physics classrooms as a teaching tool for understanding concepts such as potential and kinetic energy, periodic motion, and oscillations.

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