I am not a math major, so please forgive me if my terminology is not precisely correct. I also selected Geometry and Calculus groups for lack of a Trig option.
To better understand what is happening in a problem requiring a graphing calculator (which I do not own), I am trying to plot data to show a given damped harmonic against some limits to determine the points of intersection of those limits.
I have attached a screen cap of the given information for clarity.
Wolfram Alpha displays the base equation beautifully, but experimentation on how to word the addition of limits eludes me.
I'm hoping someone's experience can help me figure this out?
WA correctly interprets the base harmonic equation: y=e^(-x/5) cos(2pix)
Mathlabs wants me to determine at what t the harmonic exists between -0.4 and 0.4
From there I hit a wall. Please help?
Thanks in advance!
This might help. First I entered the query below.
y=exp(-x/5)*cos(2*pi*x) between y=-.4 and y=.4
This gave a picture with the graph clipped between -.4 and .4. Not exactly what was wanted, but I could see visually that the clipping was no longer in effect shortly before x=5. So I then entered this next query.
y=exp(-x/5)*cos(2*pi*x) between x=4 and x=6
If I understand the problem then the result from this second query might include what you need.
By the way, the enveloping values (local extrema) are determined from just the exponential part. So possibly you just want to know when the oscillation extrema fall in that bound independent of where it started (that is, independent of phase, which here is assumed to start at a peak at time 0). For this you just enter as below.
Wolfram|Alpha then tells you this happens around 4=4.58.
What is the input that you use for Alpha?