Question

what is differentiation of (sin wt) wrt t
actually i've confusion in shm , v2 = w2(a2 - x2) how did this equation come.

Answer 1

v^2=w^2(a^2-x^2)
take square root both side
v=+_w√(a^2-x^2)

dx/dt= +_w √{a^2-x^2}

dx/√{a^2-x^2}=+_w.dt

now integrate
integration of 1/√(a^2-x^2) =1/a sin^-1x
this is standard form of integration .
you can see your Integration chapter in 12th class.

now ,
( 1/a) sin^-1x=+_wt

(1/a)x=sin(+_wt)=sin(wt+_$)

x=asin(wt+_$)

here you see equation like as shm motion of particle in x axis which pase difference is $

Answer 2

Answer:

Explanation:

dsinwt/dt=coswt dwt/dt

w will come out and dt/dt cancel out

So it becomes coswt.w=dsinwt/dt