SIMPLE HARMONIC MOTION

Acceleration Due to Gravity

Acceleration Due to Gravity

SIMPLE HARMONIC MOTIONDaniel JamesAcceleration Due to Gravity 9/26/2015

SIMPLE PENDULUM

TABLE OF CONTENTS

I.EXECUTIVE SUMMARY3II.OBJECTIVE4III.PROCEDURE4IV.APPARATUS5V.HYPOTHESIS6VI.ASSUMPTIONS6VII.PRECAUTIONS6VIII.FINDINGS7IX.RESULTS7X.DISCUSSION9XI.CONCLUSION11XII.REFERENCE12

I. EXECUTIVE SUMMARYEverything on this planet vibrates, no matter the mass or weight things on this planet rocks back and forth in an oscillating manner. This can be simulated using a simple pendulum. By suspending a certain mass with a piece of string we can create a Simple Harmonics Motion apparatus in which we can measure how something is affected by gravity. The principle that Galileo first observed and modern technology has built upon, is how the back and forth motion of the pendulum is affected by the length of the string that bob is attached to. The back and forth motion is called the period and does not depend on the mass of the pendulum or on the size of the arc in which the string swings from. Another factor involved in the period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It follows then that a long pendulum has a greater period than a shorter pendulum.With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. All simple pendulums should have the same period regardless of their initial angle (and regardless of their masses). The period (T) for a simple pendulum does not depend on the mass or the initial angular displacement, but depends only on the length (L) of the string and the value of the gravitational field strength g.

Description of a pendulum: A simple pendulum is a rigid rod with a weight on the end of it, which, when given an initial push, will swing back and forth under the influence of gravity over its central (lowest) point.

II. OBJECTIVETo determine the acceleration due to gravity by means of a simple pendulum.III. PROCEDURE Tie the string onto the bob of brass Place the string onto the cork Secure the cork into the clamp of the retort-stand Measure the string with the metre rule to a desired height Line up the string at 90 degrees from the cork. Pull the brass while keeping the string extended downwards away from the 90 degree angle (approx. 5degrees -10degrees) Release the brass while timing with the stop watch the number of complete oscillation (maximum no# 20) Record the time (T1) Repeat for time (T2) Calculate and plot graph using formulas:T=2 (L/g)g = 4L/T2y=mx+c

IV. APPARATUS Bob of brass Length of thread Cork Stop watch Retort stand Clamp Metre rule Protractor V. HYPOTHESIS Hypothesis: As weight increases, the time will stay the same. Hypothesis: As the height of the release increases, so will the time. Hypothesis: We dont think that the length of the string will affect the time.

VI. ASSUMPTIONS The time-period in which the pendulum oscillates increases as the length of the pendulum decreases. Mass does not affect the angular acceleration while the amplitude of the sine relationship is proportional to gravity. The amplitude of the sine relationship is inversely proportional to length of the pendulum. The time-period in which pendulum oscillates does not depend on the angle of the angle of revolution if the angle is small enough.

VII. PRECAUTIONSThese precautions while measuring the period of oscillations can be done to minimize the errors during this lab:1) At the bottom of the swing, the string can stretch affecting its length and therefore affecting its period.2) The angle in which the pendulum is released from can determine the harmonic motion. The smaller the angle, the closer to harmonic motion it will behave because the restoring force is acting tangent to the arc, the pendulum moves through instead of being outside of it. Keep the angle at which you draw out the pendulum less that about 12 degrees.3) The bob material has to be taken into consideration; the pendulums mass is measured to the center of mass of the bob. A small spherical bob is much preferred over a long one. This will eliminate or minimize a greater amount of error due to air resistance.VIII. FINDINGSIn observation, the mass of the bob has no effect on the time of the pendulums oscillation and this can be proven by the use of these equations: T=2 (L/g)g = 4L/T2N.B: (According to the formulas, it shows that mass is not used) .The graph of the length of string increases so does the time ofoscillationIX. RESULTSTable 1: RECORDED DATALENGTH (M)TIME (T1) FOR 20 SWINGS/STIME (T2) FOR 20 SWINGS/STIME (T) FOR 1 SWINGS/ST^2/S^2FREQUENCY (HZ)GRAVITY

1.040.140.62.04.10.59.7

0.937.838.01.93.60.59.9

0.835.735.71.83.20.69.9

0.733.432.91.72.70.610.1

0.630.730.81.52.40.710.0

0.528.027.91.42.00.710.1

T = time for one oscillation of the pendulum (s)

l = Length of pendulum's string (m)

g = acceleration due to gravity(ms-2)X. DISCUSSION

AB=1.0-05=0.5mBC=4.07-1.96=2.11mGradient equation:y = mx + cy=4.196x -0.162In order to calculate the acceleration of gravity, I found the gradient of the time line vs. length to be m=4.196m. Calculations:g = (4)* 1/T2T^2=4.07mThe acceleration due to gravity,g = 9.7 m/s2

Acceleration due to gravity from graphValue or length= AB = 0.5mValue for T2= BC = 2.11mAB / BC = 0.236mg = (4)*(AB/BC)Acceleration due to gravity,g=9.4m/s2Acceleration due to gravity (g) at the place By calculation =9.7ms-2 From the graph =9.4 ms-2 Mean g =9.55.ms-2

Errors were made during this experiment with the reaction time. According to the T1 and T2 measurements, there are times in which the reaction time was too high or low in comparison to each other. Errors could also have been in the miscount of the amount of complete oscillation when recording 20 oscillations. In order to eliminate this error, another measurement was taken of 20 oscillations and recorded. The sum of T1 and T2 was divided by the total numbers of oscillations (40) and average was calculated. The moremeasurements taken, the less likely the final results will be erratic.My measurements confirmed my hypothesis that the period of the pendulum oscillations does not depend on the mass, either the angle of revolution, and the period of the pendulum oscillations increases as the length of the pendulum decreases. To verify that the oscillations do not depends on the mass, another material with a different mass can be used with the same length of string. The value of gravity depends on the location that the experiment was done. For example, if this experiment was done in Mexico or Denver in the U.S, the measurement of gravity would have differed from the gravity in Trinidad and Tobago.XI. CONCLUSIONMy results also show that as the length of the pendulum's stringincreases, so does the time of oscillation. I have calculated a mean value for g as 9.55 ms-2. (2s.f). this is approximately around the standard measurement of gravity of 9.8 ms-2. Therefore, we can conclude that;a) The period of the simple pendulum oscillations increases as the length of the pendulum increases.b) The period of the simple pendulum oscillations varies as square of the length of pendulum.c) The period of the simple pendulum oscillations does not depend on the mass of the load or the angle of revolution.

XII. REFERENCE(n.d.). Retrieved September 23, 2015. http://www.kbcc.cuny.edu/academicdepartments/physci/science25/Documents/Exp_2.pdf

(n.d.). Retrieved September 23, 2015. http://www.123helpme.com/view.asp?id=120352The Simple Pendulum Experiment :: Papers. (n.d.). Retrieved September 23, 2015. http://www.odec.ca/projects/2007/sard7r2/intro.htm

What precautions do we need to take while measuring time intervals using a simple pendulum? - Homework Help - eNotes.com. (n.d.). Retrieved September 23, 2015. http://www.enotes.com/homework-help/what-precautions-do-we-need-take-while-measuring-113829

8