Question

The position of x of a body is given by x=Asin (Wt). Find the time at which the displacement is maximum

Answer 1

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.