# Relationship between pendulum mass and period

### The Simple Pendulum A simple pendulum consists of a mass m hanging from a string of length L and With the assumption of small angles, the frequency and period of the pendulum. An example of this if you have problem where two pendulums are is because there will be no difference in the oscillations because mass. The illustration below explores the relationship between a pendulums period as detailed studies of pendulum physics requires knowledge of the bob's mass.

His physician friend, Santorio Santoriiinvented a device which measured a patient's pulse by the length of a pendulum; the pulsilogium. The pendulum clock The first pendulum clock In the Dutch scientist Christiaan Huygens built the first pendulum clock. This played a part in Newton's formulation of the law of universal gravitation. From this he deduced that the force of gravity was lower at Cayenne. Huygens' Horologium Oscillatorium In17 years after he invented the pendulum clock, Christiaan Huygens published his theory of the pendulum, Horologium Oscillatorium sive de motu pendulorum.

By a complicated method that was an early use of calculushe showed this curve was a cycloidrather than the circular arc of a pendulum,  confirming that the pendulum was not isochronous and Galileo's observation of isochronism was accurate only for small swings.

Temperature compensated pendulums The Foucault pendulum in was the first demonstration of the Earth's rotation that did not involve celestial observations, and it created a "pendulum mania". In this animation the rate of precession is greatly exaggerated. During the 18th and 19th century, the pendulum clock 's role as the most accurate timekeeper motivated much practical research into improving pendulums.

It was found that a major source of error was that the pendulum rod expanded and contracted with changes in ambient temperature, changing the period of swing. Huygens had discovered in that a pendulum has the same period when hung from its center of oscillation as when hung from its pivot,  and the distance between the two points was equal to the length of a simple gravity pendulum of the same period.

For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration.

## Pendulum Period

Foucault pendulum Main article: Decline in use Around low- thermal-expansion materials began to be used for pendulum rods in the highest precision clocks and other instruments, first invara nickel steel alloy, and later fused quartzwhich made temperature compensation trivial.

Clock pendulums Longcase clock Grandfather clock pendulum Ornamented pendulum in a French Comtoise clock Mercury pendulum Gridiron pendulum Ellicott pendulum, another temperature compensated type Invar pendulum in low pressure tank in Riefler regulator clockused as the US time standard from to Use for time measurement Pendulum and anchor escapement from a grandfather clock Animation of anchor escapementone of the most widely used escapements in pendulum clock.

For years, from its discovery around until development of the quartz clock in the s, the pendulum was the world's standard for accurate timekeeping. Pendulums require great mechanical stability: Pendulum clock Pendulums in clocks see example at right are usually made of a weight or bob b suspended by a rod of wood or metal a. In quality clocks the bob is made as heavy as the suspension can support and the movement can drive, since this improves the regulation of the clock see Accuracy below.

A common weight for seconds pendulum bobs is 15 pounds 6. This avoids the friction and 'play' caused by a pivot, and the slight bending force of the spring merely adds to the pendulum's restoring force.

A few precision clocks have pivots of 'knife' blades resting on agate plates. The impulses to keep the pendulum swinging are provided by an arm hanging behind the pendulum called the crutch, ewhich ends in a fork, f whose prongs embrace the pendulum rod. The crutch is pushed back and forth by the clock's escapementg,h. This force is known as inertia. What is the period of a pendulum? A period is one swing of the pendulum over and back.

What is the frequency of a pendulum? The frequency is the number of back and forth swings in a certain length of time. What variables affect the rate of a pendulum's swing? Students may come up with a variety of answers, but the four that they will be testing in this lesson are: Length of the pendulum-Changing the length of a pendulum while keeping other factors constant changes the length of the period of the pendulum. Longer pendulums swing with a lower frequency than shorter pendulums, and thus have a longer period. Starting angle of the pendulum-Changing the starting angle of the pendulum how far you pull it back to get it started has only a very slight effect on the frequency. Mass of the bob at the end of the pendulum-Changing the mass of the pendulum bob does not affect the frequency of the pendulum. Force of gravity-This accelerates the pendulum down.

The momentum built up by the acceleration of gravity causes the mass to swing in the opposite direction to a height equal to the original position. Many students believe that changing any of the variables string length, mass, or where we release the pendulum will change the frequency of the pendulum. Give them a chance to debate and discuss their answers before continuing. Where do you see pendulums in everyday life?

How are they useful? Pendulums can be found in swing sets, grandfather clocks, swinging a baseball bat, and the circus trapeze.

Pendulums are useful in timekeeping because varying the length of the pendulum can change the frequency. After your discussion, have students explore these websites: What is a Pendulum? After students have explored these sites, review with them their list of answers to the initial questions about pendulums, revising it with the current information based on the students' exploration of the websites.

## Packback cannot be run in Private Browsing

As you review their answers to the question, "What variables affect the rate of a pendulum's swing? Read More Development Begin this part of the lesson by telling students that they will explore websites to learn more about how pendulums help us learn about gravitational forces.

In the second part of the lesson, students will work in groups to construct their own pendulums and test what they have observed on the websites.

Have students run the demonstration called the Pendulum Lab. With this lab, students can 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. Make sure they understand how to run the experiment by telling them the following: With this demonstration, you can observe how one or two pendulums suspended on rigid strings behave. You can click on the bob the object at the end of the string and drag the pendulum to its starting position.

Also, you can adjust the length and mass of the pendulum by adjusting the the controls in the green box on the right side of the page. The pendulum can be brought to its new starting position by clicking on the "Reset" button. You also can measure the period by choosing the "photogate timer" option in the green box. Point out that the program measures the period, or one swing of the pendulum over and back. How does changing the length of the bob affect the period?

The shorter the length of the bob, the shorter the period will be. How does changing its starting point or angle affect the period? The smaller the angle, the shorter the period will be. How can you get the shortest period? Decrease the length, and decrease the angle. How can you get the longest period? Increase the length, and increase the angle. Explain why the pendulum continues to move without stopping or slowing down once it is set in motion.

According to the law of inertia, a body in motion will continue in motion, unless acted upon by a force. Explain the features of this demonstration to your students: In this demonstration, you can vary the length of the pendulum and the acceleration of gravity by entering numerical values or by moving the slide bar.

Also, you can click on the bob and drag the pendulum to its starting position. This demonstration allows you to measure the period of oscillation of a pendulum. To participate in this demonstration, students should follow these steps: Press the "Start" button of the stopwatch just at the moment when the pendulum is going through its deepest point.

### Why does mass not matter in a Pendulum Period? by jorden reuter on Prezi

Count "one" when it goes again through its deepest point coming from the same side. Repeat counting until "ten. Dividing the time in the display by ten yields the period of oscillation. Students can also measure the frequency of a pendulum, or the number of back-and-forth swings it makes in a certain length of time.

By counting the number of back-and-forth swings that occur in 30 seconds, students can measure the frequency directly. What is meant by the period of oscillation? It is a way of measuring the back and forth swing of the pendulum. How does changing the length of the bob affect the period of oscillation?

The longer the length of the bob, the longer the period of oscillation will be. What is meant by the acceleration of gravity? Is the acceleration of gravity always the same on earth? The acceleration of gravity is the force gravity exerts on an object. The force of gravity will always be the same on earth.

The force of gravity on other planets will be different from earth's force of gravity. How does changing the acceleration of gravity affect the period of oscillation? Increasing the acceleration of gravity increases the period of oscillation. How does changing the starting point or angle affect the period of oscillation?

• Exploring Pendulums

Increasing the angle increases the period of oscillation. What happens if you start the pendulum in an upside down position of degrees? The pendulum will not move. At this point, students should understand that gravitational forces cause the pendulum to move.

### Packback Questions

They should also understand that changing the length of the bob or changing the starting point will affect the distance the pendulum falls; and therefore, affect its period and frequency. Divide students in cooperative groups of two or three to work together to complete this activity. As outlined, students will first make predictions and then construct and test controlled-falling systems, or pendulums, using the materials listed and following the directions on the worksheet.

This controlled-falling system is a weight bob suspended by a string from a fixed point so that it can swing freely under the influence of gravity. If the bob is pushed or pulled sideways, it can't move just horizontally, but has to move on the circle whose radius is the length of the supporting string.

It has to move upward from where it started as well as sideways. If the bob is now let go, it falls because gravity is pulling it back down. It can't fall straight down, but has to follow the circular path defined by its support.

This is "controlled falling": Make sure that the groups understand that by changing the value of only one variable at a time mass, starting angle, or lengththey can determine the effect that it has on the rate of the pendulum's swing.