# Relationship between period of oscillation and length pendulum

### Pendulum - Wikipedia To understand the relationship between gravitational forces and the mass of objects, the changes . How does changing the length of the bob affect the period?. The time it takes to make complete oscillation is called the frequency 'ƒ' of the The period of a simple pendulum is directly proportional to the square root of length the relationship between the period and the length of a simple pendulum to. We are asked to find g given the period T and the length L of a pendulum. pendulum to swing and measure the pendulum's period for 10 oscillations using value for the period, based on the relation between the period and the acceleration.

For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration. 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. Each time the pendulum swings through its centre position, it releases one tooth of the escape wheel g. The force of the clock's mainspring or a driving weight hanging from a pulley, transmitted through the clock's gear traincauses the wheel to turn, and a tooth presses against one of the pallets hgiving the pendulum a short push.

The clock's wheels, geared to the escape wheel, move forward a fixed amount with each pendulum swing, advancing the clock's hands at a steady rate. The pendulum always has a means of adjusting the period, usually by an adjustment nut c under the bob which moves it up or down on the rod. Some precision clocks have a small auxiliary adjustment weight on a threaded shaft on the bob, to allow finer adjustment.

Some tower clocks and precision clocks use a tray attached near to the midpoint of the pendulum rod, to which small weights can be added or removed. This effectively shifts the centre of oscillation and allows the rate to be adjusted without stopping the clock. Pendulum clocks should be attached firmly to a sturdy wall. The most common pendulum length in quality clocks, which is always used in grandfather clocksis the seconds pendulumabout 1 metre 39 inches long. Only a few large tower clocks use longer pendulums, the 1. The wood had to be varnished to prevent water vapor from getting in, because changes in humidity also affected the length.

In the late s, Galileo began to study the behavior of falling bodies, using pendulums extensively in his experiments to research the characteristics of motion. At the time, virtually all scholars still followed the belief of Aristotle that the rate of fall was proportional to the weight of the body.

## Exploring Pendulums

Galileo showed that this conclusion was erroneous based on the fact that air resistance slowed the fall of light objects. Galileo was able to combine observation, experiment, and theory to prove his hypotheses. In easily verifiable experiments or demonstrations it can be shown that the period swing of a pendulum is independent of the pendulum's mass. It depends instead on the length of the pendulum. This would suggest that objects fall at a rate independent of mass.

The greater the amount of the unbalanced force, the more rapidly a given object's speed or direction of motion changes; the more massive an object is, the less rapidly its speed or direction changes in response to any given force. In this lesson, students will explore websites with simulations of pendulums, where they'll be able to change the length and angle of the bob and observe its effects. They will then construct and test their own controlled-falling systems, or pendulums, to further observe and verify these theories.

Read More Motivation Ask students the following questions in order to get a feel for their current knowledge and perceptions of pendulums. Answers to these questions are provided for you, but don't expect or lead students to these answers yet.

At this point, simply gather and keep a good record of students' current ideas; students will have a chance to refine these after the website exploration that follows. How would you define a pendulum? A pendulum is loosely defined as something hanging from a fixed point which, when pulled back and released, is free to swing down by gravity and then out and up because of its inertia, or tendency to stay in motion. How does a pendulum work? What are the parts of a pendulum?

A simple pendulum consists of a mass called the bob attached to the end of a thin cord, which is attached to a fixed point.

When the mass is drawn upwards and let go, the force of gravity accelerates it back to the original position. The momentum built up by the acceleration of gravity causes the mass to then swing in the opposite direction to a height equal to the original position. 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 Simple 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.

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. 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?