Physics Report Help -- Simple Harmonic motion and Elastic force

[Nancee_K]

Homework Statement

So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant) onto this sort of trampoline apparatus, and i am measuring how far the trampoline dips (amplitude)? I'm supposed to talk about the purpose of the experiment, and the relationship between my two variables, and I'm not sure as to how I should go about describing it

Homework Equations

• F= k x

The Attempt at a Solution

How does the height at which a mass is dropped, affect the amplitude of a rubber band held trampoline?
(my poor attempt)

 

[BvU]

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 ?

 

[Nancee_K]

Thanks :)
Constant: The mass of the object being dropped.

IV: Height at which mass is dropped.

DV: Amplitude of the trampoline.
More specifically, the “amplitude” discussed in the experiment, refers to the farthest length reached by the trampoline, as it dips from the landing of the mass.

 

[BvU]

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

 

[Nancee_K]

It's an exponential curve, adjusted to the amplitude averages. I'm supposed to say something like,

• The purpose of this experiment is to
  
  investigate how the period T of a pendulum depends on its length L. Period will be measured is seconds and the length in cm (this is just an example given by my teacher), but yeah I don't know how to put it into more technical terms
  

 

[BvU]

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.

 

[Nancee_K]

Right that all makes sense. Yeah I did learn about kinetic energy, but I forgot to include that with the 0.5kg mass (which is constant). And I should have included the acceleration due to gravity. I didn't think that the rubber bands necessarily counted as springs. Which equation would I even use in this case? I am unfortunately pretty bad at the SHM section we went over. Basically, I'm writing a physics IA for the IB program if you're familiar with that. I'm supposed to find the relationship between height and the amplitude, as well as equations that would help me all calculate that. Also thanks for your help.

 

[Nancee_K]

Also, the line of best fit was only put there because it fit the best

 

[BvU]

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)

Which equation would I even use in this case?

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

 

[Nancee_K]

Thanks so much for your help! I figured it out that it should be gravitational potential energy = F= kx for elastic force.

 

[BvU]

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.

 

[Nancee_K]

well not necessarily equals but I'm just supposed to explore gravitational potential energy in relation to the amplitude

 

[BvU]

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

 

[haruspex]

Also, the line of best fit was only put there because it fit the best

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?

 

[DEvens]

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.