Question

Find a model for simple harmonic motion if the position at t = 0 is 0, the amplitude is 5 centimeters, and the period is 2 seconds.

***Answer choices will be attached inside!!!

Thanks :)

Answer 1

try plugging in numbers to see which fits after your initial guess ;)

Answer 2

answer choices A,B,C,D from top to bottom :)

***my answer; C. d=5sin(pi t)

is that right? :)

Answer 3

x=5cosπt

Answer 4

d= Asin(wt)

A=5
T=2 => f=1/2

w=2pif => w=pi

Answer 5

okay, so the answer isn't C?

Answer 6

sorry x=Asinπt

Answer 7

yeah you are correct

Answer 8

answer is D

Answer 9

wait haha so is it C? or D? :/

Answer 10

Its D.

You must use sin(wt) not cos(wt)

Answer 11

its C.D is with φ=90

Answer 12

i'm confused lol

Answer 13

ohhhh okay haha so C it is? :)

Answer 14

totally

Answer 15

but did you understood why?

Answer 16

lol okay... hahaha thanks @doppler and @Diogo :)

yeah i do :)

i thought that was my answer at first, but i was a little unsure... so yeah haha b/c when they both equal 0, it has to be cosine right? it's like a rule right? and it had to be 5 cuz it's 5 cm right? :)

Answer 17

well at least i think i do haha... did i understand that correctly? LOL :/ or did i miss some stuff? :/

Answer 18

cosφ=sin(φ + 90) so it would be correct if it was x=Asin(ωt + 90)

Answer 19

as i told you on the other question the main equation is:

d = A sin (wt+phi)

where A = amplitude. If they say that amplitude is 5, then its 5 lol


When they tell you that for t=0 the position = 0 then phi = 90

Answer 20

lol okay haha thanks you guys!!!! :)

Answer 21

Well, it can't be c because the cos of 0 is 1

Answer 22

@Mertsj so the answer is or isn't C? :/

Answer 23

lol confused :P

Answer 24

IT CAN'T BE C

Answer 25

diogo the equation of SHM i think is x=Acos(ωt + φ)

Answer 26

oh okay @Mertsj haha so what would it be then?? i'm a little lost :(

Answer 27

brb, gonna get my vibrations book from college

Answer 28

When t =0, the function is 0 so it has to be D

Answer 29

from textbook...with that in mind and with initial conditions set to be φ=0 at x=0 then it would be c

Answer 30

mertsj if it says position at t=0 is 0 it means that φ=0

Answer 31

you just put φ=0 on the equation

Answer 32

\[x(t) = A e ^{-\xi \omega t}\cos(\omega t -\phi)\]

Answer 33

that s for damped motion

Answer 34

which means i was correct at first. It is D

Answer 35

Cos (0) = 1 not 0

Answer 36

but didn't y'all say when t=0 and position=0, it means it has to be cosine? :/

i'm confused hahaa so @Diogo you're saying it's D then?

not C? :/

could y'all please explain that to me?

Answer 37

Sin (0) =0 so its D

Answer 38

im pretty sure its C

Answer 39

could u pls explain like the process of how it gets to D then? cuz i'm a bit confused lol... :P

Answer 40

\[\phi = \tan^{-1} (\frac{ x(t)+\xi \omega x(0) }{ \omega \sqrt{1-\xi ^{2}} x(0) } )\]

as x(0) = 0 then phi= pi/2

Answer 41

okay... so it's between C and D right? so how can we tell whether it's cosine or sine?

Answer 42

period = pi/(2pi) = 2 So it can be C or D
Now, when t=0, the function =0
Sin(0) = 0, anything times 0 equals 0 the value of the function is 0
Cos (0)=1; 5*1=1 so the value of the function at t=1 is 5

So the answer should be D

Answer 43

d = 5 cos (pi t - pi/2)
d= 5 sin (pi t)

Answer 44

its D my bad sorry yeah its 0=Acosφ so φ=90 then it goes x=Acos(ωt + 90) =Αsinωτ

Answer 45

yes. hang on.

Answer 46

exactly

Answer 47

lol for one moment i thought that initial displacement was φ -.-

Answer 48

Oh okay, I see... Thank you so much for all your help!!!

***OS crashed on me yesterday in the middle of this problem, so I wasn't here! But it's working for me now! :) Thanks again everybody!!! :)