LAB: PENDULUM , SIMPLE HARMONIC MOTION 
What factors affect the period of a pendulum\
how to calculate the acceleration g using a pendulum



When  Galileo was only 17 years old, he used his pulse to find the period of a
swinging lamp in the Cathedral  of Pisa and discovered the  law  upon which pendulum are built.
THis illustrates the power of a lab. Physics is not just pugging numbers into equations !
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Whole numbers

 

Place value, Decimal system

3

Comparing numbers, Rounding

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Basic Arithmetic, Multiplying by powers of ten

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Factors and Divisibility

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Composite and prime numbers, prime factorization, Greatest Common factor

7

Exponents

8

Order of operation I, Multiplying by powers of 10

9

Scientific notation

10

Order of operations

11

Metric system

12

Customary length, Capacity, and Weight

13

Customary to Metric and vice versa

14

Application: Geometry

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Fractions

 

Understanding fractions

16

Equivalent fractions, Comparing fractions

17

Multiples, Least Common Multiple (LCM)

18

More comparing fractions, Finding the Least Common Denominator (LCD)

19

Adding and subtracting fractions, Simplifying , Order of operations IV

20

Mixed numbers, Improper fractions, Proper fractions

21

Mixed numbers, Adding

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Mixed numbers, Subtracting

23

Multiplying fractions

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Dividing fractions, Multiplying and Dividing Mixed numbers

25

Introduction to ratios

26

Word problems with fractions

27

 

 

 

 

 

 

 

 

 

 
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DISCUSSION
A simple pendulum consists of a mass, called a bob, connected to the end of a suspended string. When the bob is pulled to one side of its position of rest and then released, it begins to vibrate in a simple harmonic motion. We suppose the angle to be small. Each time we have a simple harmonic motion the displacement (here the displacement is angular = θ) of the object (the bob here)  is proportional to the restoring  force (the force that wants to bring back to the equilibrium position θ = 0).  Let's find out when it means.



Let's suppose the angle is small. The bob swings back and forth and there is no air resistance.
1) label the vectors. Use: W the weight, Wx (x-component of the weight), Wy (y-component of the weight) and T the tension.
2) Along the y-axis, there is no acceleration so ______________________ is balancing the ______________.
3) Along the x-axis there is an acceleration. The bob speeds up as it falls (from far right to equilibrium position), slows down as it rises again (to far left), come to a rest (far left) , then speeds up again going down. Along the X-axis Fnet = _____________. (use m,g and a trig function with θ inside).  
So the force acting on the bob to bring him back to θ =0  is just : Wx ? Wy ? N ? . This is the restoring force for a pendulum.
4) Mathematically you can show that if an angle is small then: sin (θ ) =θ. In that case. Fnet = Fx  = _________.
You just have shown that the restoring force Fnet is proportional to _________________.
Therefore, a pendulum undergoes simple harmonic motion.

5)A complete vibration (any back-and-forth motion ) is called a cycle. A cycle is the movement from some point (say the far right), to a maximum displacement in the other direction (say the far left) then back to the same point again (far right). The period (T) is the time to complete one cycle. For example, suppose 3s is required for a bob to swing back and forth, then the period of this vibration is T = ____________.

6) The number of cycles per second is called the frequency (f) . frequency = 1/ period. The unit is hertz. So if T= 3s, then the frequency = ___________.

7) The length (L) of the pendulum is measured from the point of suspension to the center of the bob. Since the bob has a radius,
L = length of the string + radius of the bob. Using a caliper measure the diameter then the radius of the bob: R = ___________________.

PURPOSE
The purpose of this lab is to investigate what factors influence the period of a pendulum. Take some guesses:
8) Do you think the mass will affect the period T? ____________  why ? ___________________________________________________________
Do you think the length of the pendulum will affect the period ? ________________________________________________________
Do you think the amplitude (the angle θ) will affect the period ? ______________________________________
Do you think a pendulum can help you to take decision?__________ finding water ? __________ find out your final grade in Physics ? __________

We will also investigate ways to estimate the acceleration due to gravity g = 9.8m/s/s using a pendulum.




PROCEDURE

step 1: Let's investigate if weight influences the period of a pendulum. Use different masses (we have only 2 here) for bobs and adjust each so the string is 100cm from the pivot point to the center of gravity of the bob. Pull the bob back to make an arc of about 15 degrees