Stuck on Applications Question

[snake86]

Ok guys I'm kinda stuck on this question and would really appreciate it if someone could give me some help?

A particular swing is pulled back and released. thereafter its displacement can be approximately described by a function of the form:

       -t/m
x=ke          cos(nt)   (btw the e is eulers no.)

where x gives the horizontal displacement of the seat of the swing in metres from the equilibrium position, t is the time in seconds, and k, m and n are arbitrary positive constants

1.Consider the first case where k=m=n=1. sketch the graph of the displacement over a suitable domain and describe its important features.

2. Systematically vary the values of k, m and n and determine the effect which each has on the behaviour of the displacement function. describe how each is related to the physical feature of the swing's motion.

3.  Determine the values of k, m and n that allow a function to best describe the swings motion.


Thx in Advance

[pHysiX]

1: plot this into your gfx calc. The t values should be t>=0 since time cannot be negative. your y-values can be negative because we are talking about displacement, not distance.

2: by doing as the qu wants, we see that the swing will start off larger and larger, and over time, the swing will have a decreasing displacement. This describes the fact that the swing is losing energy and therefore, it is osciliating but not reaching the original max height. hope that makes sense to you.

just imagine that it starts with the swing at 2, then goes down 2. but only goes up 1.5, then down 1.5 etc etc. this is just to help you understand what is happening with the horizontal displacement because since it does not go up the same as the previous, this affects the horizontal displacement.

3:hahah i have no idea for this one

good luck mate =] hope i've helped

[snake86]

Cheers mate that helped a lot

This is another part of the application question

Q4. For any given set of values of k, m, n the function has successive maxima and minima correspondency to the extreme positions on either side, find the values and displacements of these extreme positions for a selected set of values of k , m , n repeat this for some other sets of values, is there a pattern to the aspect in which the magnitudes of these displacements decrease for each set of values?

Anyone know how to do this? Also still stuck on Q3 as well.

[snake86]

Anyone? 

[pHysiX]

4: Consider k = m = n = 1

Find when there is a maximum point (x-values). Then find the y-value at those points

That should help u get started. Repeat this for increasing values of k,m,n

=]