Physics Report Help -- Simple Harmonic motion and Elastic force

Hi Nan and welcome to PF. :)

Could you give us an idea of what your two variables are ? Did you make a graph showing what you varied on the horizontal axis, and what you observed/measured on the vertical axis ? What's it look loke ?

 

Looks nice. Nice it also shows a fit result, but a fit to what (considering the a, b, c values that appear) ?

 

I suppose the sentence with pendulum is an example of how to formulate the purpose of an experiment. And if teacher gives such an example, it is probably wise to follow :)

So something along the lines of ...investigate how far an elastic sheet stretches as a function of ...

And now we come to the evaluation part: you vary the height over which the weight drops. Have you already studied things about objects falling under gravity ? like kinetic energy and such ? (I don't see it under relevant equations, so I ask). Another related subject (well, in fact very closely related) is compression of a spring under a force (your relevant equation). A spring is elastic, a (rubber?) trampoline also. What relationship do you expect to find when the weight drops in a bowl attached to the top end of a vertical spring ?

Considering the fit of the data: an exponential curve of the kind ## a\; + \; b\; \exp^{x\;c}## ? Is there any reason (except that the fit 'fits'?) for this choice ? I mean: a reasoning from theory you know that makes you expect such a relationship ? And what is the connection with the k in the relevant equation ?

Oh, and: any other parameters that might play a role ? the weight of the weight ? And the acceleration from gravity ? Shouldn't they appear in the function stretching (drop height) ?

Have to go now.

 

How much energy do you get from a weight of mass m that drops over a distance of Δh ?
How much energy does it take to compress a spring with spring constant k over a distance of Δy ?
try to wiggle these around to get a relation between height and 'amplitude'. (hint: it's not an exponential curve)

Well, if you consider it as a spring you use the spring equation. Your very own F = - k x !

 

That would be a bit strange: energy is not the same as force. Energy = force x distance. In the case of the falling weight you probably know how much energy you get from a weight of mass m that drops over a distance of Δh ?
Do you also know how much energy it takes to compress a spring with spring constant k over a distance of Δy ?

If yes on both counts, then we stumble on the next problem. But let's first check we expect the same relationship from what we think we 'know' already.

 

Can you give us an idea what the trampoline thing is ? How it works, what it looks like ?

 

OK, but best out of what list of options?
There are two parts to creating a mathematical model for a physical process:
1. Dreaming up a general form of the equation (linear, quadratic, exponential..) This will have a number of unknown presumed constants.
2. Tuning the constants to fit the data.
There's a whole area of study around this, but the most relevant rule for the current problem is "thou shalt not propose general forms that make no physical sense".
If you use some standard package, Excel say, it offers a fairly restricted set of curve fitting forms. The one that fits best might be quite wrong, while a minor variant of a more appropriate form will not be considered. E.g., if you select power law, Excel will find the best fit of the form ##Ax^\alpha##, but won't consider ##Ax^\alpha+c##.

In the present case, I have to say, the graph is surprising. Treating the 'trampoline' as a simple spring you would expect the curve to go the other way, with the slope diminishing as the drop height increases. If it is like a normal trampoline, it's a lot more complicated because the extension is not a linear function of the depth to which the sheet is depressed. That might explain it, but my instinct is that that makes it even stranger.
Your vertical axis records the vertical depression in the middle of the trampoline, right?

 

That graph worries me a bit. First it worries me because I cannot see the y-axis label. But more seriously, it worries me because the slope is increasing. I would have expected it to decrease. Can you just check that you have things plotted correctly?

Also, pay attention to what haruspex is saying. You really want to get a clear notion of the shape of the curve you are expecting. If you have a "trampoline" thing that behaves like a spring with F=kx, then your graph is the wrong shape. You will want to compare the point where the spring of the trampoline has absorbed all the energy of the kinetic energy of the mass. And the kinetic energy of the mass was gained by falling some distance. So you need to work out the energy the spring has absorbed as a function of x, and the energy the mass has gained from falling.