How long does a pendulum swing

Solution The movement of the pendula will not differ at all because the mass of the bob has no effect on the motion of a simple pendulum. PhET Explorations: Pendulum Lab Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. Click to run the simulation. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant?

Explain your answer. What is the length of a pendulum that has a period of 0. Some people think a pendulum with a period of 1. True or not, what is the length of such a pendulum? What is the period of a 1. How long does it take a child on a swing to complete one swing if her center of gravity is 4. The pendulum on a cuckoo clock is 5.

What is its frequency? Two parakeets sit on a swing with their combined center of mass At what frequency do they swing? What is its new period? A pendulum with a period of 2. What is the acceleration due to gravity at its new location? At what rate will a pendulum clock run on the Moon, where the acceleration due to gravity is 1.

The length of the string affects the pendulum's period such that the longer the length of the string, the longer the pendulum's period. This also affects the frequency of the pendulum, which is the rate at which the pendulum swings back and forth.

A pendulum with a longer string has a lower frequency, meaning it swings back and forth less times in a given amount of time than a pendulum with a shorter string length. This makes that the pendulum with the longer string completes less back and forth cycles in a given amount of time, because each cycle takes it more time.

The mass of the bob does not affect the period of a pendulum because as Galileo discovered and Newton explained , the mass of the bob is being accelerated toward the ground at a constant rate — the gravitational constant, g.

Just as objects with different masses but similar shapes fall at the same rate for example, a ping-pong ball and a golf ball, or a grape and a large ball bearing , the pendulum is pulled downward at the same rate no matter how much the bob weighs. Finally, the angle that the pendulum swings through a big swing or a small swing does not affect the period of the pendulum because pendulums swinging through a larger angle accelerate more than pendulums swinging through a small angle.

This is because of the way objects fall; when something is falling, it keeps accelerating. As long as an object is not going as fast as it can, it is speeding up. Therefore, something that has been falling longer will be going faster than something that has just been released. A pendulum swinging through a large angle is being pulled down by gravity for a longer part of its swing than a pendulum swinging through a small angle, so it speeds up more, covering the larger distance of its big swing in the same amount of time as the pendulum swinging through a small angle covers its shorter distance traveled.

Watch this activity on YouTube. Ask the students to explain which factors might affect the period of a pendulum. Answer: Pendulum length, bob weight, angle pendulum swings through.

Which factor s really do affect the pendulum's period? Answer: The length of the pendulum. Why does the weight not make a difference? Answer: Because the pendulum, just like falling objects, is not dependent on weight. How does the length of a pendulum's string affect its period? Answer: A pendulum with a longer string has a longer period, meaning it takes a longer time to complete one back and forth cycle when compared with a pendulum with a shorter string.

Also, the pendulum with the longer string has a lower frequency, which means it completes less back and forth cycles in a given amount of time as compared with a pendulum with a shorter string. Why does the angle the pendulum starts at not affect the period? Answer: Because pendulums that start at a bigger angle have longer to speed up, so they travel faster than pendulums that start at a small angle.

One oscillation is complete when the bob returns to its starting position. Count the votes and write the totals on the board. Give the right answer. Human Matching: On ten pieces of paper, write either the term or the definition of the five vocabulary words. Ask for ten volunteers from the class to come up to the front of the room, and give each person one of the pieces of paper.

One at a time, have each volunteer read what is written on their paper. Have the remainder of the class match term to definition by voting.

Have student "terms" stand by their "definitions. As a library research project, have the students research Galileo Galilei. What other scientific findings did he make during his lifetime? Have the students' research the ways that engineers use pendulums today.

Some suggestions: seismographs, inertial dampeners, in sky-scrapers. The tension in the string of a pendulum is clearly a force of constraint. Sure, the direction of this tension force is in the same direction as the string but the magnitude changes to whatever value it needs to be to keep the mass at the same distance from the pivot point.

This means that in order to make a numerical model for a pendulum, you need to use a trick. There are three different ways you can model the motion of a pendulum. I have looked at these methods before, so let me just give a short review. Notice that the title of that post is "a third way. If you assume the mass is confined to move in a circular path, then you can reduce this to a one dimensional problem with the angle of the pendulum as the only variable.

The only force that changes this angular position is the angular component of the gravitational force. There is a simple solution to this differential equation by assuming a small amplitude of oscillation and thus a small angle. The problem with the pendulum motion is that the tension is a constraint force. Well, what if we make it a deterministic force?

If the string is replaced with a very stiff spring, it should be an easier problem. This method can work fairly well. Here is a numerical model that displays the angular position for both method 1 and 2. View Iframe URL. Just click the "play" button to run this. Two pendula with different lengths will different periods; the pendulum with the longer string will have the longer period. A pendulum stops oscillating because it loses energy when it is converted into heat.

Even without air friction, the friction which exists with the point around which the pendulum rotates causes the system to lose kinetic energy and eventually stop. When the pendulum is at rest, not swinging, it hangs straight down. It was potential energy because the washer could swing due to its relative position and gravity.

This kind of potential energy is known as gravitational potential energy. A pendulum works by converting energy back and forth, a bit like a rollercoaster ride. If there were no friction or drag air resistance , a pendulum would keep on moving forever. In reality, each swing sees friction and drag steal a bit more energy from the pendulum and it gradually comes to a halt. When you let go of the ball, it swings downward like a pendulum. As it starts swinging, the energy changes from potential energy to kinetic, or moving, energy.

Since the total energy has to stay constant, the kinetic energy of the ball must be zero and the ball must stop moving. Frictional forces also cause the mass on a spring to lose its energy to the surroundings. In some instances, damping is a favored feature. So the conservation of energy does not violates, only the energy stored in pendulum transferred to the surrounding, so the total energy remain conserved.

When the pendulum stops briefly at the top of its swing, the kinetic energy is zero, and all the energy of the system is in potential energy. When the pendulum swings back down, the potential energy is converted back into kinetic energy.

The truly conserved quantity is the sum of kinetic, potential, and thermal energy.