The displacement of a body executing SHM is given by x = A sin (2 $π t$ + $\frac{π}{3}$ ). The first time from t = 0 when the velocity is maximum is:

Question

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Answer 1

The displacement of a body executing SHM is given by:
$x = A s i n (2 π t + π / 3)$
Velocity, $v = \frac{d x}{d t} = 2 π A c o s (2 π t + π / 3)$
For maximum velocity,
$\frac{d v}{d t} = 0$

$\Rightarrow - 4 π^{2} A s i n (2 π t + π / 3) = 0$
$\Rightarrow s i n (2 π t + π / 3) = s i n (n π)$
$\Rightarrow 2 π t + π / 3 = n π$
for $n = 1$
$\Rightarrow 2 π t = π - π / 3 = \frac{2 π}{3}$
$t = \frac{1}{3} = 0.33 s e c$
The correct option is A.

Answer 2

The displacement of a body executing SHM is given by:

x = A s i n (2 π t + π / 3)

Velocity,

v = \frac{d x}{d t} = 2 π A c o s (2 π t + π / 3)

For maximum velocity,

\frac{d v}{d t} = 0

\Rightarrow - 4 π^{2} A s i n (2 π t + π / 3) = 0

\Rightarrow s i n (2 π t + π / 3) = s i n (n π)

\Rightarrow 2 π t + π / 3 = n π

for

n = 1

\Rightarrow 2 π t = π - π / 3 = \frac{2 π}{3}

t = \frac{1}{3} = 0.33 s e c

The correct option is A.