Simple Harmonic Motion Lab

Physics Simple Harmonic Motion Lab

Introduction

All objects have a natural frequency at which they like to vibrate. Think about a playground swing and how you have to time your pushes in order to get it to reach a maximum height above the ground. You are providing your pushes at the natural frequency of the swing which science people call the "resonance frequency" of the object/system.

You are now about to embark on an experiment that investigates vibration motion. Think of systems that vibrate and you will immediately become aware of the usefulness of this investigation. What do you think automobile engineers who design shock absorbers have to be aware of or an architect involved in the design of a concert hall? The music you hear from an instrument or stereo system is also the result of vibration?

Experiment

Set up the equipment according to the following diagram. You will investigate the motion of an oscillating (vibrating) spring by using a motion detector positioned so to read the vertical displacement over time. In this investigation you will use our knowledge of vibrating springs to determine the spring force constant.

Experimental Setup

Part 1: Procedure

i. Prepare the computer for data collection by opening “02 Spring.cmbl” from the Physics with Vernier experiment files of Logger Pro. Two graphs will appear on the screen. The vertical axis of the distance graph is scaled from 0 to 1.5 m. The vertical axis of the velocity graph is scaled from – 1 to + 1 m/s. The horizontal axis of both graphs has time scaled from 0 to 10 s.

ii. Place the motion detector so that it is facing upward, about 1m below a mass suspended from the spring. Put a protective cage over the motion detector.

iii. Attach the spring to the pulley and put a small mass from your weight set on the end of the spring so that when you pull it down a couple of cm and let it go, the mass oscillates up and down and not side to side. Find the mass of the spring plus added mass and write it in the data table. Pull the mass down again and let it go. Press and record the motion of the mass over time.

iv. If you do not see a smooth graph, the mass most likely was not in the beam of the Motion Detector. Adjust the aim or look for interfering objects and try again. You might want to try sticking a small index card to the bottom of the mass or change the distance between the mass and the motion detector if the graph persists on being jagged. Print when you have a good graph. Make sure it has an appropriate title and your name(s) are on it as a footnote!

Part 1: Questions

1. Find the time taken for one complete oscillation. (note: can select examine from the analyze menu or drag over the correct interval and read the Dt in the bottom left of the screen). Enter this value in your results table. Check this value using the multiple peaks on your graph. Using other peaks write down four other values for this time in the space provided. Then find the average time and record it. We call this time the period.

2. Is the period constant or does it change with time?

3. What indicated by your graph changes with time?

4. Using the period find out how many vibrations there are per second.

5. What effect does pulling the mass down more (or less) have on the period? Make a prediction and then investigate this question. Try to explain what you observe. Go to experiment – store latest run. You can use Data –Hide Data Set to toggle between graphs.

Results Table

Part / Total Mass (kg) / Period 1 (s) / Period 2 (s) / Period 3 (s) / Period 4 (s) / Average Period (s) / k
(N/m)
1
2
Finitial
(N) / xinitial
(m) / Ffinal
(N) / xfinal
(m) / DF
(N) / Dx
(m) / k
(N/m)
3

Part 2: Procedure

You will now determine the spring force constant k, by measuring the period for various masses.

I. Add more mass to your spring and repeat part 1. Record your data in the table. Determine the average period.

II. Repeat for three more masses on your spring. Do not overstretch the spring!

Part 2: Questions

1. From your notes you should have seen the following theoretical expression:

T = 2p Ö(M/k) Rearranging for k we get

k = M (2p/T)2

For each mass and period grouping determine the k value of the spring. Record your values in the table.

2. Determine the average k value for your spring using the values in your table.

Part 3: Procedure

I. You will now find the spring constant (which tells you how many Newton’s of force are needed per unit distance of stretch) the easy way, and compare it with your answer above.

You will need a meter stick and a spring scale. Lay the spring horizontal and apply two different forces with the spring scale. Use the meter stick to measure the end position of the spring for each force. Record your measurements in the data table. Be careful NOT to overstretch the spring!

Part 3: Questions

1. Find the spring constant according to:

k = Change in applied force (DF)

Extension of the spring (D x)

k = ______N/m

2. Determine the percentage difference between you answers for k found from

parts 2 and 3.

% difference = difference in k value x 100 %

average of the two

% difference = ______

3. Account for any differences between your two values for k found in parts 2

and 3

Simple Harmonic Motion Lab Answer Sheets

Name ______Date______Hr. ___

Show all work for the calculations needed to answer each question. Attach your graphs to the back of this packet

Results Table (10 pts)

Part 1

1. Find the time taken for one complete oscillation. Show calc! (2 pts)

2. Is the period constant or does it change with time? (1 pt)

3. What indicated by your graph changes with time? (1 pt)

4. Using the period find out how many vibrations there are per second. Show calc! (2 pts)

5. What effect does pulling the mass down more (or less) have on the period?

Prediction (2 pts)–

What you found out: include period values (3 pts) –

Explanation of observation (3 pts)-

Part 2

6. Show below example calculations of k for two different masses and periods in your table. Follow the step method! (4 pts)

7. Average k value of your spring = ______N/m (2 pts)

Show calc!

Part 3

8. Value of k from physical measurement ______N/m (3 pts)

Show calc!

9. Percentage difference between your answers for k found from parts 2 and 3.

(3 pts) Show calc!

10. Account for any differences between your two values for k found in parts 2

and 3 (3 pts)