Damping of an mechanic oscillator.

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Damping of an mechanic oscillator

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. The pendulum swang back and forth and as the mass-spring system, these oscillations got their displacement slowed down as the time got on. I noticed a small sound for this experiment too.

  1. Metre ruler

I forced a 100.0cm ruler to oscillate by placing one of its ends on edge of lab desk. I pushed the other end verticaly downwards and released it. Here again the displacement decreased but particularly in a faster way and got back to its original position after a few seconds. The sound is sharper this time.

Interpretation

All of this examples show the same pattern of movement. The mass of pendulum speeds up from 0 (accelerates) as it moves at the centre of the oscillation. It is moving fastest as it reacheas the centre. It then slows down again (decelerates) as it moves towards the end of the oscillation. When it comes back, it no longer reaches the same displacement it started with. The displacement is now a bit less than the one at the beginning of the motion. This is due to its collision with air molecules. Air molecules try to stop its motion. Its speed decreases and so there is a lost of kinetic energy. Kinetic energy Ek=(1/2)mv2 (in Joules J) where m is the mass (in kilogram) of the small sphere and v its velocity (in metre per second ms-1). The change in kinetic energy is Ek=(1/2)m(v)2 where v is the change in velocity. These collisions with air molecules are therefore inelastic. Since energy is not lost but transformed (2nd law of thermodynamics), the deficit of energy is released as sound and heat. Eventually, if you touch the mass of pendulum after a certain amount of time, you will noticed that it has warmed up sligthly.

Particularly with the meter ruler, we can see that the displacement decreases faster at the beginning and tends to slow down as it approaches the centre of the oscillations. This is due to the fact that the meter ruler has a much larger surface area than the mass of pendulum colliding with air molecules.

There is a non constant transfer of energy between the two forms: kinetic to potential energy. Potential energy is maximum at the beginnin of the motion. It decreases, transfering to kinetic energy as the mass of pendulum accelerates towards the centre of oscillation where it becomes completely transferred to kinetic energy. Kinetic energy is then maximum. As the mass decelerates after it passes the centre, kinetic energy is transferred back to potential energy. The mass has a new maximum potential energy, less than it started with. And the same transfer of energy from potential to kinetic happens again as the mass goes back.

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Independent variables  

I repeated the experiment of the metre ruler but this time I reduced the length (from the edge of the desk to itd end. I noticed it was faster than when I used the full length and the sound got larger. I reduced the length evn more and what I could conclude is that <the longer the length, the slower it will oscillate>.

I now used a steel blade (with a smaller thickness and width) and this was too fast and oscillated many times but and stopped in an unmeasurable time to me. ...

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