Question

A kipping robe under constant vibation has a 5.0cm amplitude and an 8.0 second period. Wat vertical position is the rope at when t = 5.0s?

b) Find two times when that same rope's position is +2.0 cm.

c) Draw 2 cycles of this wave

Answer 1

So, we know that the rope is making a sin wave right with a amplitude of 5 and period of 8 sec. We know that the sin wave has a period of 2pi and aplitude of 1. You need to change the amplitude and period of the sine wave to simulate the rope, then plug in 5 to find the height. The form y= A*sin(x).

Answer 2

what equation would I use?

Answer 3

Well, the amp is 5 so 5*sin(x) and now for the period is changed by changing x. Thus x now pi*x/4

Answer 4

how do we know what x is?

Answer 5

plug pi*x/4 into x. so y= 5*sin(pi*x/4). and solve by putting 5 in for x to find the height.

Answer 6

I got 1.25

Answer 7

nvm I got 0.3423...is that right?

Answer 8

Help please!

Answer 9

i got -3.54. Is your calc in radians?

Answer 10

no should it be?

Answer 11

and how can it be negative? the vertical position can be negative?

Answer 12

Yes, your calc needs to be in radians to get the position of height. When you graph a sin wave it makes a wave above and below the x-axis right? So even though the value you get is negative its realy just 3.54 units away from the x-axis. can you graph sin(x)?

Answer 13

alright makes sense, how about B?

Answer 14

okay, so the sin wave periodic which means that the function y= 5*sin(pi*x/4) repeats over and over again. So their asking when is the rope at a height of positive 2 (above the x axis).

Answer 15

so I would put 2 in for x?

Answer 16

no x is time not height. so when is time = 2

Answer 17

you mean when is height = 2?

Answer 18

basicly 2=y= 5*sin(pi*x/4) and solve for x or just graph it and trae when height is 2.

Answer 19

How would I graph it ?

Answer 20

if you have graphing calc in the y editor put 5*sin(pi*x/4).

Answer 21

Would the answer to b) be approx 3.46?

Answer 22

I plugged my answer in on http://www.meta-calculator.com/online/

Answer 23

Ya. looks close to what I got. but there are 2 others.

Answer 24

approx 0.528?

Answer 25

and approx -4.5?

Answer 26

i ment 1 other

Answer 27

so 0.528?

Answer 28

0.5568*?

Answer 29

Yes .528 is close to what i got.

Answer 30

how can I find those numbers out using equations?

Answer 31

not the negative answer because the rope frequency is from 0 to 8 sec.

Answer 32

ah okay

Answer 33

how can i find that .528 and 3.46 with equations?

Answer 34

let me see

Answer 35

Okay, so you set y= 5*sin(pi*x/4) to 2. 2= 5*sin(pi*x/4). then divide 5 so 2/5=sin(pi*x/4). Now use arcsin on both sides to undo sin then isolate x by multipling by 4/pi on both sides.

Answer 36

I get 30? :S

Answer 37

arcsin0.4 = 23.46

Answer 38

okay, x= sin^-1(2/5)*(4/pi) = .524

Answer 39

I plugged exactly that in and i get 30.02

Answer 40

oh i was in degrees that explains it

Answer 41

how can I get the other spot?