I need help finding the equation of a sine function, I know (-.75,0) to (.75,0) is one period and (.75,0) to (2.25,0) is another so based on that I was able to solve for "b" by applying the equation Period = 2pi/b so in that case 1.5=2pi/b, and therefore b=4.189, im stuck finding "a" and if there was any horizontal shift left or right, or any vertical shift up or down.

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I need help finding the equation of a sine function, I know (-.75,0) to (.75,0) is one period and (.75,0) to (2.25,0) is another so based on that I was able to solve for "b" by applying the equation Period = 2pi/b so in that case 1.5=2pi/b, and therefore b=4.189, im stuck finding "a" and if there was any horizontal shift left or right, or any vertical shift up or down.

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so one period is 1.5 right? the other is 1.5 right?
yup
2pi ---- = 1.5; w = 2pi/1.5 right? w

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yup, w=4.189
without knowing anything more about the wave, or the graph there is no wayto determine the amplitude
since y=0 when the period happens we can assume its not lifted
since it is symetric about the orgin it aint shifted either
well, can I give you the rest of the points? it's a sine function essentially but with changing amplitude and period so my teacher suggested first getting the equation for the maximum values and then for a period piece and adding the two together does that make sense?
giving all the information to a question is usually a good way to get an informed answer ;)
hahha ok one second and I will type the points out.
A=(Max - min)/2
(-.75,0,) ...(-.5, -.7906) ....(0,0) ..... (.25, .90461),.... (.5, .94868) ....(.75, 0) ...(1, -1.039),... (1.25, -1.088) ...(1.5,0).... (1.75, 1.1915) .....(2,1.2471) and (2.25, 0)
(0,0) use sine and no phase shift
\[.75sin(4.189x)\]?
how did you figure "a" as .75?
oh because i was wrong. sorry
range from -.75 to 2.25 yes?
yup
i have to write hold on
ok
range has length 3 yes?
yes
so you need 1.5 out front
so it will have range of length 3
then it goes from -.75 to 2.25 so at the end you will need to add .75
this will take you from - .75 when the function is -1 (or rather -1.5) up to 2.25 when the function is 1 (or 1.5)
so far we know it looks like \[y= 1.5 sin(___) +.75\]
now we have to figure out what goes inside.
b=4.189
i meant \[y=1.5sin ( ?)+.75\]
period = 2pi/b and period we found was 1.5 right? so solve for b and its 4.189
that takes care of period yes?
wait let me check hold on
ok
oh no i am all messed up. i had the range at 3 but that is wrong wrong wrong. the range goes from smallest y value to biggest. what is the smallest y value?
ok here maybe I can explain it better because I am trying to break this up as my teacher suggested, the full graph of what I need the equation for looks like the green graph on this link: http://www.google.com/imgres?imgurl=http://fan.lib.ru/img/z/zharow_a/evolution_continues/majatnik_kachajasx_bez_trenija.jpg&imgrefurl=http://fan.lib.ru/z/zharow_a/evolution_continues.shtml&usg=__uANt4T4noENBP-ROlSIgJEg9idI=&h=253&w=787&sz=51&hl=en&start=0&zoom=1&tbnid=L3R1ovN3yt9ifM:&tbnh=67&tbnw=208&ei=2RDkTc2gDsb00gHgms2cDg&prev=/search%3Fq%3Dgrowing%2Bamplitude%26um%3D1%26hl%3Den%26biw%3D1080%26bih%3D535%26tbm%3Disch&um=1&itbs=1&iact=hc&vpx=74&vpy=231&dur=243&hovh=127&hovw=396&tx=210&ty=90&page=1&ndsp=15&ved=1t:429,r:5,s:0&biw=1080&bih=535
does that link work if not i can find another
http://www.ltcconline.net/greenl/courses/204/appsHigherOrder/forcedVibrations.htm
that links better scroll down to the graph, see it?
oh man i was way way off base. the last graph?
where it says y=tsin(10t)? that graph
not the graph at the very bottom, where it says y=tsin(10t)
ah i see it
yeah so thats the shape of what I am working with and I given the following 12 points: (-.75,0,) ...(-.5, -.7906) ....(0,0) ..... (.25, .90461),.... (.5, .94868) ....(.75, 0) ...(1, -1.039),... (1.25, -1.088) ...(1.5,0).... (1.75, 1.1915) .....(2,1.2471) and (2.25, 0)
so amplitude changes
yes and period too
oh lord i have no friggin idea how to model this. let me think
well what my teacher recommended is finding the exponential equation of the maximum values and then finding the equation for a period piece like we were just trying to do and then adding the two functions together if that makes sense if not we can try any other way yoou can come up withh
well there is no exponential part of the picture you just sent. that is the last graph
if you connected just the maximum values it is..
are you looking at the right graph its the graph right before "Forced Vibrations with Damping"
i have to confess that i really have no idea how to do this
oh ok..

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