RYERSON UNIVERSITY

DEPARTMENT OF PHYSICS

LAB REPORT

FOR

PCS 125 SECTION 05

TITLE OF EXPERIMENT: The motion of a Pendulum

EXPERIMENTERS: 1) Meet Shah: 500396229

2) Gurdeep Saini: 500406572

3) Joshua Dylan Gracias: 500413913

AUTHORS OF THIS REPORT: 1) Meet Shah

2) Gurdeep Saini

3) Joshua Dylan Gracias

EXPERIMENT PERFORMED ON: 9th February, 2011

REPORT SUBMITTED ON: 16th February, 2011

TA’S NAME: Timothy Luk

Intro and Objective:◊ The main purpose to conduct this experiment is to,

1. Measure the position and velocity as a function of time for an oscillating mass and spring system.

2. Compare the observed motion of a mass and a spring system to a mathematical model of simple harmonic motion.

3. Determine the amplitude, period, and a phase constant of the observed simple harmonic motion.

◊ In addition to linear motion and rotational motion, there is another kind of motion exist which is the motion of oscillations and vibrations.

◊ When something oscillates or vibrates, it moves back and forth with the time. One simple system that vibrates is a hanging mass from a spring.

◊ In above system, simple harmonic motion occurs when a motion of mass on a spring is subject to the linear elastic restoring force given by Hooke’s law (Figure 1). The force applied to the hanging mass by an ideal spring is proportional to how much the spring is stretched or compressed.

F s=−kxF s (N) is a restoring force because it is always directed toward the equilibrium position and

therefore opposite the displacement (x ) of the block from equilibrium. k (N/m) is a constant called the rate or spring constant.

◊ There are certain characteristics involved with the Simple harmonic motion. The amplitude (A) of the motion is simply the maximum value of the position of the particle (mass in our case) in either positive or negative direction. The constant (ω) is called angular frequency, which is a measure of how rapidly the oscillations are occurring; the more oscillations per time, the higher

the value of(ω). the angular frequency can be modeled by ω=√ km where m is the mass in

kilogram.

◊ The period of the motion (T ) is equivalent to T=2πω

. The inverse of the frequency is called

frequency ( f ) which represents the number of oscillations the particle undergoes per unit time

interval. The units for frequency are cycles per second or hertz (Hz). f=1T

=2πω

. Now,

rearranging the equation gives ω=2πf . ◊ The simple harmonic motion of the mass hanging by the spring and its position can be modeled

by the equation below,y=Asin (2 πft+φ )

In this above equation, y is the vertical displacement from the equilibrium position, A is the amplitude of the motion, f is the frequency of the oscillation, t is the time, and φ is a phase constant.

◊ Secondary purpose of the experiment also include the,1. Examination of the energies involved in simple harmonic motion.2. Testing of the principal of conversation of energy.

◊ The oscillating mass system can also be described from an energy perspective. For this experiment, two kinds of energies have been taken into consideration.

◊ The mass (m) , with velocity (v) can have a kinetic energy KE,

KE=12mv2

◊ The spring can also hold elastic potential energy PE,

P Eelastic=12k y2

Here, (k ) is the spring constant and ( y ) is the extension or compression of the spring measured from equilibrium position.

◊ The principal of the conversation of energy tells us that total amount of energy remains constant over time. That is,

∆ KE+∆P Eelastic=0

Procedure:Part I: POSITION AND VELOCITY IN SHM

The station was already set up to perform the first part of the lab. The program Logger pro was set up with the necessary document which is used to conduct the

lab. First the preliminary run was made to be sure the equipments were working fine by just lifting

the mass up and letting the spring oscillate while the logger pro program was working. First the 200 g of mass was used with the initial amplitude of 5 cm to let the spring oscillate. Initially the spring was set in motion and after the program Logger pro was started and the data

was recorded by the motion detector and graph appeared on the screen. The graph was set to record data for 10 seconds. The position graph was like a sinusoidal curve. The graph was used to record the amplitude, phase shift, period, frequency. Steps IV to VII were repeated again for 200g mass and 10 cm amplitude and 300g mass with 5

cm amplitude. The observation was recorded in the provided table. After performing this, the damping experiment from the extension was performed. A sheet of paper was attached at the end of the 300 g mass. Then the spring was set to 5 cm of amplitude and the in the program logger pro the graph was

set to record for 120 seconds. The graph was observed and the data was recorded.

Part II: ENERGY IN SHM

The station was already set up to perform the second part of the lab. The program Logger pro was set up with the necessary document which is used to conduct the

lab part 2. First the mass of 50 g is used attached to spring and was left hanging motionless. The weight

was calculated using F=mg and was entered in the data collection in the Logger pro. The mass was increased by 50 g for each trial up till 300g, and the weight was also calculated

and entered in the table. Then in the logger pro program the linear fit button was clicked and the k value was found using

the magnitude of the slope. Another document was opened in logger pro and then the value of k was set in the file. The mass was left hanging with little to no oscillation at all and the motion detector was

calibrated. Then the mass of 200g was used and was oscillating at the amplitude of 10 cm. The data was recorded on sheet of paper and the graph was observed.

Extensions:

1. Total Mechanical Energy = 12mv2+1

2k y2+mgh

References: S e r w a y , R a y m o n d A . , & J e w e t t , J o h n W . ( n . d . ) . P h y s i c s f o r s c i e n t i s t s a n d e n g i n e e r s

w i t h m o d e r n p h y s i c s [ E i g h t E d i t i o n ] .

R e p o r t g u i d e l i n e s . ( n . d . ) . R e t r i e v e d f r o m

h t t p : / / w w w . r y e r s o n . c a / p h y s i c s / c u r r e n t / l a b _ i n f o r m a t i o n / p r o c e d u r e s _ g u i d e l i n e s /R e p o r t % 2 0 G u i d e l i n e s . p d f

S i m p l e h a r m o n i c m o t i o n . ( n . d . ) . R e t r i e v e d f r o m

h t t p : / / w w w . r y e r s o n . c a / p h y s i c s / c u r r e n t / l a b _ i n f o r m a t i o n / e x p e r i m e n t s / P C S 1 2 5 /S H M . p d f