Question

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.

Answer 1

so one period is 1.5 right?

the other is 1.5 right?

Answer 2

yup

Answer 3

2pi
---- = 1.5; w = 2pi/1.5 right?
w

Answer 4

yup, w=4.189

Answer 5

without knowing anything more about the wave, or the graph there is no wayto determine the amplitude

Answer 6

since y=0 when the period happens we can assume its not lifted

Answer 7

since it is symetric about the orgin it aint shifted either

Answer 8

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?

Answer 9

giving all the information to a question is usually a good way to get an informed answer ;)

Answer 10

hahha ok one second and I will type the points out.

Answer 11

A=(Max - min)/2

Answer 12

(-.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)

Answer 13

(0,0) use sine and no phase shift

Answer 14

\[.75sin(4.189x)\]?

Answer 15

how did you figure "a" as .75?

Answer 16

oh because i was wrong. sorry

Answer 17

range from -.75 to 2.25 yes?

Answer 18

yup

Answer 19

i have to write hold on

Answer 20

ok

Answer 21

range has length 3 yes?

Answer 22

yes

Answer 23

so you need 1.5 out front

Answer 24

so it will have range of length 3

Answer 25

then it goes from -.75 to 2.25 so at the end you will need to add .75

Answer 26

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)

Answer 27

so far we know it looks like \[y= 1.5 sin(___) +.75\]

Answer 28

now we have to figure out what goes inside.

Answer 29

b=4.189

Answer 30

i meant \[y=1.5sin ( ?)+.75\]

Answer 31

period = 2pi/b and period we found was 1.5 right? so solve for b and its 4.189

Answer 32

that takes care of period yes?

Answer 33

wait let me check hold on

Answer 34

ok

Answer 35

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?

Answer 36

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

Answer 37

does that link work if not i can find another

Answer 38

http://www.ltcconline.net/greenl/courses/204/appsHigherOrder/forcedVibrations.htm

Answer 39

that links better scroll down to the graph, see it?

Answer 40

oh man i was way way off base. the last graph?

Answer 41

where it says y=tsin(10t)? that graph

Answer 42

not the graph at the very bottom, where it says y=tsin(10t)

Answer 43

ah i see it

Answer 44

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)

Answer 45

so amplitude changes

Answer 46

yes and period too

Answer 47

oh lord i have no friggin idea how to model this. let me think

Answer 48

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

Answer 49

well there is no exponential part of the picture you just sent. that is the last graph

Answer 50

if you connected just the maximum values it is..

Answer 51

are you looking at the right graph its the graph right before "Forced Vibrations with Damping"

Answer 52

i have to confess that i really have no idea how to do this

Answer 53

oh ok..