An object is in simple harmonic motion with the equation of motion as x=Acos(ωt+φ),when t=T/2,the velocity of the object is......?
Gives
"x=Acos(wt+\\phi)\\rightarrow(1)"
A=amplitude
Phase="\\phi"
Angular frequency=w
equation (1) differencuate with respect time
Velocity
"v=Awsin(wt+\\phi)"
t=0
"v=Awsin\\phi\\rightarrow(2)"
"t=\\frac{T}{2}"
"v=Awsin(\\frac{2\\pi}{T}\\times\\frac{T}{2}+\\phi)"
"v=Awsin(\\pi+\\phi)"
"v=Awsin\\phi\\rightarrow(2)"
equation (2)and(3)are same
Point P wave equation
"t=\\frac{T}{2}" Velocity of object
"v=Asin\\phi"
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