 #1
 467
 30
 Homework Statement:

Object doing S.H.M , displacement ##D(t)=Asin(\omega t)##
where A is amplitude, ##\omega## is the angular frequency. Speed of object is v when displacement is half of the amplitude. Find speed in terms of v when displacement is 0
 Relevant Equations:
 NIL
My workings:
##D(t) = Asin\omega t##
##v(t) = \frac{\text{dD}}{\text{dt}}=Acos(\omega t)\omega##
##v(t) =Acos(\omega t)\omega##
When displacement half of amplitude,
## Asin\omega t## = 0.5##A##
## sin\omega t## = 0.5
##v(t) =Acos(\omega t)\omega##
##v(t) =\omega (0.5Asin\omega t)cos \omega t ##
##v = \omega (0.5A*0.5)cos \omega t##
Pretty confused here on what I should do to proceed on. Any ideas?
##D(t) = Asin\omega t##
##v(t) = \frac{\text{dD}}{\text{dt}}=Acos(\omega t)\omega##
##v(t) =Acos(\omega t)\omega##
When displacement half of amplitude,
## Asin\omega t## = 0.5##A##
## sin\omega t## = 0.5
##v(t) =Acos(\omega t)\omega##
##v(t) =\omega (0.5Asin\omega t)cos \omega t ##
##v = \omega (0.5A*0.5)cos \omega t##
Pretty confused here on what I should do to proceed on. Any ideas?