# Page 1 of 5 Hooke’s Law – Simple Harmonic Motion PhET Simulation Lab ______________________________________________________________________________ Lab Writeup created by Prof. M. Jain Objectives 1....

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Hooke’s Law – Simple Harmonic Motion
PhET Simulation Lab
______________________________________________________________________________
Lab Writeup created by Prof. M. Jain
Objectives
1. To determine the average spring constant k of a spring within a certain extension range.
2. To investigate the dependence of the period T on the hanging mass m.
3. To compare the experimental period with the calculated period assuming simple harmonic
motion.
4. To show that the period T is almost independent of the amplitude for assumed simple
harmonic motion.
Introduction
When an object is suspended on a spring the spring stretches. The extension of the spring
depends on the weight of the object and the “stiffness” of the spring (see Figure 1). We will
assume an ideal situation that the extension of the spring x is proportional to the weight of the
hanging object F. The spring obeys Hooke’s Law.
(1)
The negative sign here emphasizes that the force acting on the object is a restoring force.
The spring constant k expresses the stiffness of the spring.
If the mass of the spring and the air resistance is negligible and the spring obeys Hooke’s
Law, then the motion of the object is simple harmonic. The vibration period T depends on the
hanging mass m and the spring constant k.
XXXXXXXXXX2)
Part I: Determination of the average spring constant
springs_en.html
1) Click on Lab.

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2) You will be directed to the screen as shown to the right.
3) You can select the tools to measure the length from the
toolbox in the right.
4) Measure the original length of the spring Lo (this will be
the constant).
5) Change the mass by sliding the bar and observe the new
length.
6) Record the new length Lo in the table below.

XXXXXXXXXXF= - K ΔL Hooke’s Law
XXXXXXXXXXF = mg where, g = 9.8 m/s^2
XXXXXXXXXXΔL = L – Lo
7) Include the screenshot of any one trial

Data Table 1
Data Analysis
8) Calculate k using Hooke’s Law
9) Find k-average
10) Plot the graph of F vs ΔL and obtain the best fit line.
11) What does the slope represent?
12) Show work for the findings from the slope below.
Activity:
13) Find the mystery masses by placing them on the spring, measuring the stretch and using
the average k value that you obtained from the step (5). Label them m(blue) and m(pink)
M (kg) F (N) Lo(m) L (m) ΔL (m) K (N/m)
=
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Part II: Determine the dependence of period on the hanging mass
1. We will again use the same PhET simulation for this part.
2. Select the tools by clicking on the checkboxes as shown in the picture. (Make
sure the damping is set to none and gravity is selected for the Earth).
3. With a hanging mass of 0.100 kg on the spring, pull the mass down vertically by
about 2 cm, and then release the mass. Use a timer (stopwatch) to time 10
complete oscillation and then find the period of one oscillation. (Note: you can
customize the mass by sliding the bar to the right or left)
4. Repeat above Procedure with a hanging mass of 0.140, 0.180, 0.220, 0.260, and
0.300 kg.
5. Include the screenshot of any one trial

Data Table 2
Trial
No.
m
[kg]
??ℎ?????????
Using equation 2
[s]
????
(for 10 oscillations)
[s]
????
(???? = ??????? 10 /10)
[s]
Texp2
[s2]
1 0.100
2 0.140
3 0.180
XXXXXXXXXX
5 0.260
6 0.300
Data Analysis
6. Calculate the theoretical periods using equations (2) with the hanging masses used in steps
(4) and (5).
7. Compare the experimental and theoretical periods with a table like the following.

Trial
No.
m
[kg]
exp
[s]
TTh (equ-2)
[s]
%
Difference
1
2
3
4
5
6
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8. Square both sides of Equation (2) we can obtain

?2 = 4?2
?
?

Graph T2 vs. m and find the slope a of the best-fit straight line.

Compare with

9. What does the slope represent?
10. Find k from the slope and show your work.
11. Compare the value of the spring constant found in part II with the experimental value
determined found in part 1 and find the % difference.

Part III: Determine the dependence of the period on the vibration amplitude.
12. With one hanging mass, say, 0.300 kg, increase the amplitude to 4 cm. Find the period.
Compare with the period when the amplitude was 2 cm. Is there any notable difference?
m = 0.260 Kg T (exp)
[s]
A=2cm
A=4cm
Questions:
1. If your spring were stiffer, what effect would it have on the period for a given mass?
2. From your observation of the hanging mass, at what point in its motion is its speed the
greatest? The magnitude of its acceleration? The magnitude of its displacement?
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References
1. Physics for Scientists and Engineers, 6th edition, Paul A. Tipler and Gene Mosca,
(W. H. Freeman, New York, NY, 2008).
2. Physics: Foundations and Applications, Robert M. Eisberg and Lawrence S. Lerner,
(McGraw-Hill, NY, NY, 1981).
3. Engineering Mechanics Statics and Dynamics, 6th Edition, Russell C. Hibbeler, (MacMillan,
NY, NY, 1992)