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# The experiment involves the determination, of the effective mass of a spring (ms) and the spring constant (k).

Extracts from this document...

Introduction

Investigation of the Properties of a Spring 14/11/99.

## Introduction

The experiment involves the determination, of the effective mass of a spring (ms) and the spring constant (k).

It is known that the period (T), of small oscillations of a mass (m) at the end of a helical spring is given by the formula:

T= 2π(m+ms)

k

In this experiment the same clamp was used for all readings to make sure there were no miss-readings taken due to differences in the way the clamp and stand reacted to the movement of the mass.  Also the spring in all readings was the same as, after all the ms and k of two different springs is going to be different and lead to different readings.

The things that were varied in the experiment were, the number of slotted masses on the end of the spring and the number of oscillations of the mass to be counted.   The number of oscillations (T) will be measured using a stopcock.  Which was varied to give a number between 20 and 30.   To keep the number of oscillations, for every mass as similar to each other as possible.  To help keep the experiment fair.

So to find ms and k the following experiment was devised and carried out:

Middle

25.3

600

25

26.9

27.0

26.95

These were the trial readings taken before the experiment, they were taken to help in the decision of the size of the limits.  The readings are shown in the order that they were taken.  They were taken in this order, to check that the masses, which were to be used were usable.   i.e. the smaller masses did not oscillate to quickly to be measured and that the larger masses did not damage the spring.  Hence the order of the readings.

 Mass/Kg x number of oscillation’s Time for x oscillations( in seconds) xT av/s T/s T2/s2 ΔxT/s % unc in xT % unc in T2 ΔT2/s2 0.1000.2000.2500.3000.4000.4500.5000.600 5040353025302525 xT xT xT 23.3425.9825.0523.3322.0428.3024.6526.88 0.470.650.720.780.880.940.991.08 0.2210.4230.5180.6080.7740.8890.9721.158 0.10.10.10.10.10.10.10.1 211513131111109 4230262622222018 0.0930.1270.1350.1580.1700.1960.1940.208 23.6225.8625.0123.3522.0128.2524.6726.89 22.6126.3325.0923.3722.0128.3224.6126.88 23.8025.7525.0623.2622.0928.3424.6626.86

Procedure/Method

When planning the experiment, there were two methods of obtaining information about the spring, which were discussed one being the one decided upon.  The other being a way of finding out the spring constant (k), by just measuring the extension (x) of the spring, with different sized weights attached to the spring. Which would have given a straight-line graph going through the origin, where the gradient of the line would give the value k.

As shown in the graph below:

###### Graph of Force/N against  Extension/m for a spring

This experiment was chosen over the other one, as not only can k be found but ms

Conclusion

2 = 2 × % unc in xT2

To find the value of ΔT2/S2 the following formula was used, ΔT2/S2 = T2/S2 × % unc in xT2

100

Conclusion

The graphs show that the formula, T2= 4π2m+4π2ms   does indeed give a straight-line graph of form Y = mx + c.

k         k

The graphs show that the value of ms = 0.025 +/− 0.1 kg  and the value of k = 20 +/− 6 N/m

The objective of this experiment was to determine ms and k of a spring which has been done within the limits, 0.125 and − 0.075 kg for ms and  26 and 14 N/m for k.

## Critical Analysis of Results

The experiment could have been improved in the following ways:

1. More readings for each mass could have been taken to get a more accurate mean value.
2. A greater range of masses could have been used to get a more accurate trend line for the graph.
3. There could have been more time for the experiment, so that the readings etc would not be so rushed
4. The bounces of the spring could have somehow been restricted to the vertical.
5. The measurement of time could be improved, by using a light beam connected to a timer to measure the time.  The apparatus could be set up so that at the bottom of one oscillation the weight would break the beam and start the timer then at the start of the next the weight would break the beam and stop the clock.  This would give a more accurate measurement of time.

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