Question

simple harmonic motion dynamics

Answer 1

@kirtishukla first of all,

\[\huge \color{green}{\text{WELCOME TO OPENSTUDY!}}\]

Answer 2

Hmm - Physics?

Answer 3

now this section is specially for math questions, so its adviced you close this question and post it in physics section .Also be a bit more clear in your question.

Answer 4

Well I believe physics questions should be allowed in mathematics section , physics is afterall an application of mathematics.

Answer 5

Yes, but this is more of a physical question than it is mathematical.

Answer 6

agreed with shubhamsrg

Answer 7

well,

\[\large \rm \boxed{x=a \cos (\omega t+\phi )}\]

is the displacement time equation of SHM in which A,\(\omega \),and \(\phi\) represent amplitude,angular frequency and phase constant respectively.

Answer 8

no this is from my dynamics book

Answer 9

ok @kirtishukla did you understand that?

Answer 10

ya i knew that one but that is of physics part iam asking abt maths one

Answer 11

can you provide the exact question you have?

Answer 12

\[x=a \cos \sqrt{?u} t \] t\]

Answer 13

question mark inside root?

Answer 14

nothing is there qstion mark is by mistake

Answer 15

did you mean

\[\LARGE \boxed{x=a \cos \sqrt{ut}}\]

Answer 16

t is out from underroot u

Answer 17

ok :) @ParthKohli was actually practising along with answering

Answer 18

what do you understand when you compare this with the displacement time equation of SHM?

Answer 19

@kirtishukla ?

Answer 20

here phase difference is not present

Answer 21

i wanna simply ask when double differntiation of x with respect to t is taken equivalent to -kx then why - sign is taken

Answer 22

second derivative is taken to get equation of velocity

Answer 23

why - sign is taken

Answer 24

differential of \[\cos \theta =?\]

Answer 25

*"derivative" is better term

Answer 26

gt it @kirtishukla ?

Answer 27

here is a nice document on SHM that can help you

http://www.physnet.org/modules/pdf_modules/m25.pdf

Answer 28

-sin \[-\sin \]

Answer 29

that is why equation of velcoty contains negative sign

Answer 30

*velocity

Answer 31

*velocity

Answer 32

but iam asking abt hey just hav the visit of bsc part 2 dynamics then topic shm then re tell me

Answer 33

bsc ? maybe a friend of mine can help.... i am in high school :)
@nitz can you take a look?

Answer 34

do u know complex exponentials?

Answer 35

no

Answer 36

I'll take the physics approach here....since you're asking for the minus sign
are you familiar with vectors?
in this case, please note that the second derivative of the sine wave equation will result in \(a=-\omega^2x\) [i'm taking that u know this]
from a simple horizontal spring mass system SHM,

now, there would be force acting in the different direction as the velocity and the displacement.
so, taking the displacement direction as +ve,
\(\Sigma \vec F= \vec F_s =m\vec a\)
\(-kx=m(-\omega^2x)\) [note that in F=kx, while the displacement is +ve, the force itself is -ve]
so it will be \(\omega = \sqrt \frac{k}{m}\)