Simple Harmonic Motion

SIMPLE HARMONIC MOTION : PENDULUM SCIENTIFIC CONCEPTS A pendulum is any mass which swings back and forth on a rope, string, or chain. Pendulums can be found in old clocks and other machinery. A playground swing is a pendulum. If you pull the mass away from its rest position, so that the string is at an angle, and then let go, the mass will begin to swing back and forth. The length of time it takes the mass to swing all the way over and back,once is called the period of the pendulum. In these experiments, the dependent variable will always be the time for one full swing, or the period. The three independent variables will be the mass, the angle, and the length of string. The controlled variables will be the attachment point of the string, the string itself, the method used to time the pendulum, and the variables we are not currently testing. These will remain the same for each test, so that we know they won't affect the results. In this experiment, the variables that we will tested is the length of string.

length of string 20 30 40 45 50 55

trial 1 32.72 31.56 30.58 30.26 29.24 27.82

trial 2 32.99 31.77 30.59 30.12 28.27 27.91

trial 3 32.89 31.66 30.84 30.41 28.84 27.86

average 32.87 31.66 30.67 30.26 28.78 27.86

UNIQUE FEATURE OF THIS ACTIVITY 1) This data can be manipulated easily. For example, we can just enter the data in the table the time of one oscillation; the value of the average can be calculated. 2) Data displayed in a systematic manner, so that we save a lot of time in drawing graph and show relationship between time and the length of string. 3) Spreadsheet is very practical for repetitive calculation. For example, the point of graph will also automatically change according to the change of the data. 4) So that, we do not waste our time recalculation and re-graphing and can continue to do more important things like analyzing the data or graph.

ENGAGE

(A)

What do you think of the picture? In picture (A), what happen when the pendulum is move?

(B)

EMPOWER

Steps: 1) Students are given: • • • • • • • • •

One retort stand One G-clamp Two bosses Pendulum bob 100cm thin flexible string Two small blocks of wood Meter rule Half meter rule Stop watch

2) Students are required to plan an experiment to determine the effect of length of strength on the one oscillation. 3) Students have to construct hypothesis in this experiment. 4) You may give this instruction to construct the activity: •

• • •

Decide what angle you will use to set the pendulum swinging. Mark it on the wall behind the release point. Set up the full length of string with one weight on the end. Length= 20 cm, 30 cm, 40 cm, 45 cm, 50 cm, 55 cm

Make and record measurements to determine the period of these oscillation. Generate your own table

Questions: 1) Calculate the value of T using this given formula: T = π2 g

x T

2π +

y g

ENHANCE

From the experiment, can you give the application of the pendulum Answer: 1) Clocks The most common application of the pendulum is to use its regular motion to control the motion of the hands of a clock. This is still seen in the older grandfather clocks. Every time the pendulum goes back and forth, it moves a gear one notch. Gears are then used to move the hands of the clock. 2) Foucault Pendulum Another interesting application is called the Foucault Pendulum. This pendulum will demonstrate the Earth's rotation. The Foucault Pendulum is a very large pendulum that is often several stories high. The reason it is so large is so that it will keep swinging over a longer period of time. Friction forces often damp a smaller pendulum and cause to finally stop after a relatively short time.

The picture below shows the size of the pendulum and the scale at the bottom to indicate the positions at different times of the day. To explain how the Foucault Pendulum works, consider putting a pendulum exactly at the North Pole or South Pole. While the Earth rotated on its axis, the pendulum would continue to swing in the same direction in space. It would appear as if the pendulum was slowly changing directions, but in reality it is the Earth that is revolving underneath the pendulum. This same phenomenon will happen at locations other than the poles, except that the reason is not as obvious.