# Pendulum string and ball question

• osustudent2010
In summary, the conversation discusses a problem with a simple pendulum involving a 0.58 m long string and a small ball. The question is how much time elapses before the ball attains its greatest speed after being released from rest. The frequency is calculated to be .654 cycles/sec and the greatest speed is achieved when the pendulum is completely vertical. The person in the conversation is seeking help and is told to use T/4, which is the definition of a period of oscillation.
osustudent2010
Hi! Here is a phyics problem I am having trouble with:

A simple pendulum is made from a 0.58 m long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?

so far the only thing I've found is the frequency = .654 cycles/sec
i know its greatest speed would be when the pendulum is completely vertical (theta = 0), I just can seem to relate the two

any help would be appricated! thanks!

You need this baby: T/4.Do you know why?

Daniel.

P.S.What's the definition of a period of oscillation...?

Hi there! Thanks for reaching out with your physics problem. Let's see if we can work through it together.

First, let's define some variables to make things clearer. Let's say that the length of the string is L = 0.58 m, the angle the ball is pulled to is θ, and the time it takes for the ball to reach its greatest speed is t.

We know that the frequency of a simple pendulum is given by f = 1/T, where T is the period of the pendulum. The period is the time it takes for one full cycle, or one swing from one side to the other and back again. In this problem, we are given the frequency, f = 0.654 cycles/sec, so we can find the period by taking the inverse: T = 1/f = 1/0.654 = 1.53 seconds.

Now, to relate the period to the time it takes for the ball to reach its greatest speed, we can use the formula for the period of a simple pendulum: T = 2π√(L/g), where g is the acceleration due to gravity, which is approximately 9.8 m/s^2. We can rearrange this equation to solve for t: t = T/4 = π√(L/g)/2 = 0.766 seconds.

So, it will take approximately 0.766 seconds for the ball to reach its greatest speed after it is released. This makes sense because the ball will reach its greatest speed when it is at the bottom of its swing, which is half of a full cycle.

I hope this helps! Let me know if you have any other questions or if anything is unclear. Good luck with your physics problem!

## 1. How does the length of the string affect the motion of a pendulum?

The length of the string affects the period, or time it takes for the pendulum to complete one full swing, of a pendulum. As the length of the string increases, the period also increases. This is because the longer string allows for a larger arc, leading to a longer distance for the pendulum to travel in one swing. Additionally, a longer string also reduces the frequency, or number of swings per unit of time, of the pendulum.

## 2. What factors influence the motion of a pendulum?

The motion of a pendulum is influenced by several factors, including the length of the string, the mass of the ball, the angle at which the pendulum is released, and the strength of gravity. Other factors such as air resistance and friction can also affect the motion of a pendulum.

## 3. How does the mass of the ball affect the motion of a pendulum?

The mass of the ball affects the period of a pendulum. A heavier ball will have a slower period than a lighter ball, as the increased mass requires more energy to move. However, the mass of the ball does not affect the frequency of the pendulum.

## 4. Why does a pendulum eventually come to a stop?

A pendulum eventually comes to a stop due to the effects of air resistance and friction. As the pendulum swings back and forth, it experiences resistance from the air and friction from the pivot point, causing it to lose energy and eventually come to a stop.

## 5. Can a pendulum be used to measure time accurately?

Yes, a pendulum can be used to measure time accurately. In fact, pendulum clocks were once the most accurate timekeeping devices available. The period of a pendulum is constant, making it a reliable tool for measuring time. However, external factors such as temperature and air resistance can affect the accuracy of a pendulum clock.

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