The position of x of a body is given by x=Asin (Wt). Find the time at which the displacement is maximum
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Answer:
The position x of a body is given by :
x=A\sin \omega tx=Asinωt
To find,
Time at which the displacement is maximum.
Solution,
For maximum displacement put \dfrac{dx}{dt}=0
dt
dx
=0
\begin{gathered}\dfrac{dx}{dt}=\dfrac{d(A\sin \omega t)}{dt}\\\\\dfrac{dx}{dt}=A\cos \omega t{\cdot} \omega\\\\A\cos \omega t{\cdot} \omega=0\\\\\cos \omega t=0\\\\\omega t=(2n+1)\dfrac{\pi}{2}\end{gathered}
dt
dx
=
dt
d(Asinωt)
dt
dx
=Acosωt⋅ω
Acosωt⋅ω=0
cosωt=0
ωt=(2n+1)
2
π
if n = 0
\begin{gathered}\omega t=(2n+1)\dfrac{\pi}{2}\\\\\omega t=\dfrac{\pi}{2}\\\\t=\dfrac{\pi}{2\omega}\end{gathered}
ωt=(2n+1)
2
π
ωt=
2
π
t=
2ω
π
Hence, this is the required solution.
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