Physics - Spring Oscillations Lab

8/9/2019 Physics - Spring Oscillations Lab

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Introduction:

The purpose of this lab was to examine Hookes law and inestigate the proportionalit! of force"

distance traelled" and the uni#ue properties of an oscillating spring with an attached mass$ Hookes law "

gien b! the e#uation % & kx" states that the restoring force '%( of an extended or compressed spring is

proportional to the distance of compression or elongation 'x(" and is affected b! the springs constant of

proprtionalit! 'k($ The experiments were designed to inestigate whether real-world spring behaior

would conform to Hookes law$ )t is h!pothesi*ed that obserations of the oscillations of a mass moing

the spring 'harmonic motion( can be used to calculate the spring constant uni#ue to the spring$ Minimal

error between experimental 'obsered( and theoretical 'actual" calculated( spring constants will support

the h!pothesis$

Procedure:

The experiment consisted of

two exercises inestigating

oscillations of a mass on a spring$ +

force sensor was mounted to a ring

stand and base" with the force

measuring hook pointed

perpendicular to the table surface$ +

spring was hung from the hook" with

a mass suspended from the spring$

,ulling down on the mass initiated

ertical oscillating motion" with data

recorded b! ata Studio on the computer through an S./01 interface$

Data:

T : period of Oscillation 's(

m: mass 'kg(

x: distance 'm(

t: time 's(

2: initial drop angle 'degrees(

g: 3$45 'm6s7(

% & ma '8(

% & kx

k & mg6x '86m(

= km and =2 Tkm=2T

(2

T)2

=

k

mk=m

(2

T)2

Sinusoidal function:

Asin [ 2 (xC)B ]+D 9 & T


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,ercent rror: |ObservedExpectedExpected |x100


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xercise 5:

Table 5:

Mass (kg) Force (N) Displacement (cm) Displacement (m)

1$15 1$134 ;$; 1$1;;

1$17 1$53<


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xercise 7:

Table 7:

Mass (kg) Period (s) T2/42

1$17 1$0;4 1$11/

1$1; 1$raph 7: Linear

0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05 0.050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

f(x) = 3.29x - 0

R = 1

Exercise 2: Mass vs T2/42

T2/42

Mass (k)


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>raph ; ? 0cm displacement 'Sinusoidal function: Sine of best fit(

>raph = - 71cm displacement 'Sinusoidal function: Sine of best fit(


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nal!sis

xercise 5 recorded the force and displacement of the spring$ Hookes law" F=kx " can be

rewritten as k=F

x 'where % is e#ual to the mass times grait!( to sole for the unknown spring

constant$ +nal!sis of the slope of >raph 5 reeals the expected spring constant 'k( to be ;$7raph 7 reeals the obsered spring constant 'k( to be ;$7435 86m$

The percent difference between the experimental and theoretical k alues was calculated as

1$41C" indicating that the spring behaed according to Hookes law and all measurements were recorded

accuratel!$

|ObservedExpectedExpected |x100|3.2891N/m3.263N/m3.263N/m |x 100=0.80 Error

"onclusion:

@omparison of the resistance to force 'k( of the spring and the springs behaior during harmonic

oscillations reealed conformance to Hookes constant within expected error and standard deiation$

Theoretical calculations assume the spring to be massless and hae no effect on the period$ The percent

error between k alues" howeer slight" reeals that the spring mass is important in real-world conditions$

Successful experimental identification of the spring constant within standard deiation of the theoretical

alue supports the h!pothesis that obserations of the oscillations of a mass moing the spring 'harmonic

motion( can be used to calculate the spring constant uni#ue to the spring$ )mproements to consistenc!

when inducing oscillations and inclusion of the spring mass will further minimi*e the experimental error$

Oerall the experiments successfull! demonstrated the conformit! of harmonic spring motion to Hookes

law$


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#ncertaint! $ummar!

Predicted (a%k%a% &'pected) alue:

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>raph 0 ? Max6Min for xercise 5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

f(x) = 3.25x - 0.01

R = 1

f(x) = 3.27x - 0.01

R = 1

f(x) = 3.26x - 0.01

R = 1

Exercise 1: Force vs. Displacement

Displacement (m)

Force (N)

>raph < ? Max6Min for xercise 7

0 0.01 0.02 0.03 0.04 0.05 0.06

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

f(x) = 2.73x + 0.01

R = 1

f(x) = 4.12x - 0.02

R = 1f(x) = 3.29x - 0

R = 1

Exercise 2: Mass vs T2/42

T2/42

Mass (k)

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Physics - Spring Oscillations Lab