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Damping of an mechanic oscillator.

Extracts from this document...

Introduction

Introduction

An object oscillates when it moves back and forth repeatedly, on either side of some fixed position (centre). If we stop it from oscillating, it returns to it original position. This sort object is called an oscillator. Vibrations exist in two types: free and forced. An object experiences forced oscillations when its frequency (number of vibrations per second) is not its natural frequency of vibrations. If its frequency of vibrations is its natural one, it will then experience free vibrations.

When the amplitude of oscillations of an object remains the same as it goes back and forth, the oscillations of that object are harmonic. And if the amplitude decreases instead, it is said that oscillations are damped and the phenomenon is called damping.

In this experiment, I will study what might affect damping and then measure it.

Study of some oscillators

1. A mass-spring system

I set using a tall stand, springs, a hanger and three 50gram masses, a system that I got to oscillate. I hold and displaced slightly the masses vertically downwards making sure I don’t deform any of the springs and released it. As a let it oscillate for a few minutes, I noticed that the displacement (from the originial position) of the oscillations was deceasing for the system of masses tended to return back to its original position. The room in which I processed this experiment but I could hear a small sound caused by the conpression and extension of springs.

1. A pendulum

I set a piece of string of about a metre long that I rolled and attached one end on a cork pad, and at the other end I fixed a small sphere mass. I pull the mass some distance sideways and let it go.

Middle

t1/2

t1/2

t1/2

Modifications and improvement

The reading of the amplitude was generally bad since marks on the scale are too close together an the chances to read (human judgement) the wrong one were high. Using a graph paper stuck on the table (it would move if not), we can draw lines of fixed amplitudes. A maximum amplitude of 10.0cm to allow the steel blade to oscillate for a considerable time before we start recording measurements.

1. Timing

I could not feel confident with the time since each signal was suddent, and so the reaction time of the timer high. We wanted reaction  to be as small as possible so that our experiment would be reliable. To do that, when I had to record the time, my partner would say to me <get ready>, <get ready>, <it’s near>, <it’s near>, <almost there>, <NOW!>. I would have had enough time to concentrate and focus on starting and reseting the stopclock and so my reaction time would be very small. I had to the same for my partner when she had the turn to measure the time. To estimate the reaction time, we did a very simple test using a ruler. I vertically hold the lower end of the ruler (assumed to be 0cm). My parner hold a stopclock. She said: <get ready>, <steady>, <NOW!

Conclusion

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To find the average half life, I summed them all then divided by 4.

t1/2(average) = (57.5s + 57.5s+ 60.0s + 57.5s)/4 = 58.1s

The relation relating half life and decay constant is t1/2(average) = 0.693/λ so

58.1= 0.693/λ and then λ = 0.693/58.1s = 0.0119s-1

 Half life measured t1/2 (s)t1/2 initial    t1/2 final       t1/2 Average half file t1/2               (s) Decay constantλ    (s-1) 17.5 75.0 57.5 58.1 0.0119 75.0 132.5 57.5 132.5 192.5 60.0 192.5 250.0 57.5

10             55          102.5                    150               250

45         45              47.5                50

t1/2(average) = (45.0s + 47.5s + 47.5s + 50.0s)/4 = 47.5s

λ = 0.693/47.5s = 0.0146s-1

 Half life measured t1/2(s)t1/2 initial    t1/2 final       t1/2 Average half file t1/2               (s) Decay constantλ(s-1) 10.0 55.0 45.0 47.5 0.0146 55.0 102.5 47.5 102.5 150.0 47.5 150.0 200.0 50.0

7.5           42.5                75                 110            145

35s        32.5s        35s                   35s

1/2(average) = (35.0s + 32.5s + 35.0s + 35.0s)/4 = 34.4s

λ = 0.693/34.4s = 0.0201s-1

 Half life measured t1/2 (s)t1/2 initial   t1/2 final       t1/2 Average half file t1/2               (s) Decay constantλ  (s-1) 7.5 42.5 35.0 34.4 0.0201 42.5 75.0 32.5 75.0 110.0 35.0 110.0 145.0 35.0

12.5                   50           87.5           124.5         162.5

37.5s               37.5s           37s            38s

t1/2(average) = (37.5s + 37.5s + 37.0s + 38.0s)/4 = 37.5s

λ = 0.693/37.5s = 0.0185s-1

 Half life measured t1/2 (s)t1/2 initial    t1/2 final       t1/2 Average half file t1/2               (s) Decay constant λ    (s-1) 12.5 50 37.5 37.5 0.0185 50 87.5 37.5 87.5 124.5 37 124.5 162.5 38

5                 29                             53              76                    100

24s              24s              23s         25s

t1/2(average) = (24.0s + 24.0s + 23.0s + 25.0s)/4 = 24.0s

λ = 0.693/24.0s = 0.0289s-1

 Half life measured t1/2 (s)t1/2 initial   t1/2 final       t1/2 Average half file t1/2               (s) Decay constant  λ(s-1) 5.0 29.0 24.0 24.0 0.0289 29.0 53.0 24.0 53.0 76.0 23.0 75.0 100.0 25.0

0               24              46                      68              94

24s            22s        22s                    26s

t1/2(average) = (24.0s + 22.0s + 22.0s + 26.0s)/4 = 23.5s

λ = 0.693/23.5s = 0.0295s-1

 Half life measured t1/2 (s)t1/2 initial   t1/2 final       t1/2 Average half file t1/2               (s) Decay constant λ(s-1) 0.0 24.0 24.0 23.5 0.0295 24.0 46.0 22.0 46.0 68.0 22.0 68.0 94.0 26.0

Theory

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