can you explain find how do I find the elongation of the spring m for part 1

and how to find the period of T

part 2 can you help explain how to find everything

I just need help trying to understand the lab and explain it

Mass of spring:________________

M0 Suspened Mass (kg)	F= M0 g Force (N)	x Elongation of the spring (m)
.200	Take as 0	Take as 0
.300	(.300-0.200) x 9.80 =
.400
.500
.600
.700
.800

99

Hung mass:	200 g	350 g	550 g	700 g
Time for 50 cycles (sec) amplitude #1
Time for 50 cycles (sec) amplitude #2			j
Time for 50 cycles (sec) amplitude #3
Average of three above times (sec)
Period, T (sec)
T2 (sec2)

100

LABORATORY EXERCISE # 8 Part II Data Sheet : Simple Pendulum Date ______________

Name:______________________________ Partners:__________________________ Instructor's Signature:___________________________

Nominal length Of pendulum, L	100 cm	60 cm	30 cm
Actual length, L
Time for 50 oscillations (sec)
Period, T (sec)
T2 (sec2 )

LABORATORY EXERCISE # 8C

To study the force law for a spring (Hook's Law). To verify the equation for the period of a vibrating spring.

Equipment and Supplies

Spring, support for suspending spring, set of weights, stop clock, meter stick, balance.

(a) Unstretched spring (b) Stretched spring

M

M

(c) Force diagram T= k x

Mg35

x

Discussion

When a stretching forceFis applied to a spring, the elongation of the springxis found to be proportional toFif the elastic limit is not exceeded. The force is arestoringforce,

i.e., always opposite to the displacement. This empirical law is called Hook's law:

F=kx wherekis called theforce constant,or thestiffnessof the spring. The general equation

of motion for the massMwith accelerationawhich is vertically hung from the spring as seen in the figure is

Ma=Mgkx within the elastic limit. Here, we completely neglect the mass of the spring which in our

experiment is much smaller than the mass attached. (1) If the massMis in an equilibrium state, the equation is reduced to

Mg=kx sincea=0. The elongationxof the spring can be measured as a function of the weight

hung on it when varying the massMof the suspended weightF=Mgand a plot of F vs x is a straight line, as illustrated below.

Elongation x (m)

36

Force F (N)

The slope of the straight line is the stiffnesskof the spring. In the MKS units it isN/m.

(2) If a mass,M, hung from the end of an elastic spring is pulled down and released, it will oscillate up and down. This is an example ofsimple harmonic motion. The accelerationamust not be neglected since the mass is not in equilibrium. In this case the equation of motion is rewritten as

x +Mkx=gwherex=aand the displacement at timetis

x=g+Acos(t)2

=Mk replaced byt+2/, then the displacement x is unchanged. This means that the

where displacement has the same value after timeT,

depends on the massMand the stiffness of the spring. If the timetis

T=2=2Mk.

This is the period of the oscillation.Ais the amplitude of the oscillation andis determined by the initial displacement of the mass.

Actually, since all parts of the spring also execute simple harmonic motion, the mass of the spring needs to be included in some way. Since not all parts of the spring execute the full motion, it turns out thatm', the "effective mass" of the spring is just 1/3 of the full inertial mass,m. So, the parameterMshould be the sum of the mass of the hung weight,M0, plus 1/3 of the mass of the spring:

M=M0+m' = M0+m/3

where,M0is the mass of the suspended weight,mis the mass of the spring, and

m'is the effective mass of the spring (m'=m/3).Procedure

1.Fvs.xdata. Measure the elongationxof the spring as a function of the weight hung on it. mass of the suspended weight from 200 grams to 800 grams in 100 g steps. position when 200 g is suspended to be zero displacement ( the origin).

Vary the Take the

Do not exceed 800 g.

37

2.T vs. M data. Hang a mass of 200 grams from the spring and make at least three determinations with a stop clock of the time for 50 complete oscillations of the mass. Use a different initial amplitude in each determination. Repeat with masses of 350, 550 and 700 grams.

Calculations and Conclusions

A.From the data in Procedure1, calculate analytically and graphically the force constant of the spring and compare the two values. The analytic calculations involve using Hook's law for each of your data points. The graphical method involves plottingF vs. x, and measuring the slope of the best straight line through the data points (see the sketch above).

B.PlotT2vs. M, i.e., the square of the period on the vertical axis and the mass of the suspended weight on the horizontal axis. From the graph, calculate the value of the stiffnessk.

C.Compare the values ofkfound inAandB. This means, by what percent do they differ? Now, in summary, considering both measurements, what is the precision (expressed as a percent) of your measurement ofk?

D.Does the period of simple harmonic motion depend on the amplitude? How well does your data justify your answer ?

38

LABORATORY EXERCISE #Part II: The Simple Pendulum

8

Objective

To study how the period of a simple pendulum depends on its length. acceleration due to gravity in the laboratory room.

Equipment and Supplies

To measure the

Metal sphere suspended by a fine string, stop clock, meter stick, vernier calipers.

Discussion

Asimplependulum is one where all the mass is concentrated at a small "bob". A good approximation is made by using a massive weight held with a light string from a sturdy support. If the motion is restricted to "small angles", the motion is closelysimple harmonic. T, the period of the motion, depends only on the length of the string, and the acceleration of gravity. Surprisingly, the period does not depend on the value of the

T=2Lg(1)

suspended mass:

where,Tis the period of oscillation. Lis the distance from the support point to the center of the massive bob, andgis the local acceleration due to gravity.

Procedure

1.Tvs.Ldata. Adjust the pendulum so thatLis about 100 cm. MeasureLusing the meter stick and vernier calipers. Determine the time for 50 oscillations with the amplitude of motion less than 10.

2.Repeat Procedure1.using a length approximately 30 cm, and again withLabout 60 cm.

Calculations and Conclusions

A.Plot your data asT2vs. L. The theory, given by Eq. (1), predicts that your data points should fall on a straight line of slope 2/g. Thus by measuring the slope of the best straight line fit, you can pull out the value ofgin the lab. What is the value ofgyou39

obtain, and what is the precision you claim for your measurement ( expressed as a percent) ?

B.You have just finished measuringg, the acceleration due to local gravity. Express your result as in the form wxy z %. In exercise #2, several weeks ago, you also measuredg, using an entirely different method. For the two results summarize the following information:

a) claimed precision b) agreement with accepted value

Do the two results agree? The key here is the criterion you used to answer the question. Add any further relevant comments.