The displacement of an object attached to a spring and executing SHM is given by x- 2 - 10-2 cos - m- In what time the object attains maximum speed first-

x = 2 × 10^ 2cosπ t v = dxdt = 2 × 10^ 2×π×sinπ t Now, v to be maximum, sinπ t should be 1 Or, π t = π2 ∴ t = 12 #160; = ...

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Standard XII

Physics

Velocity Displacement Relationship

The displacem...

Question

The displacement of an object attached to a spring and executing SHM is given by $x = 2 \times 10^{- 2} c o s π τ m$ . In what time the object attains maximum speed first?

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Solution

$x = 2 \times 10^{- 2} cos π t$
$v = \frac{d x}{d t} = - 2 \times 10^{- 2} \times π \times sin π t$
Now, $v$ to be maximum,
$sin π t$ should be $1$
Or, $π t = \frac{π}{2}$
$∴ t = \frac{1}{2} = 0.5 s e c$

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The displacement of an object attached to a spring and executing SHM is given by x=2×10−2cosπτm. In what time the object attains maximum speed first?

x=2×10−2cosπtv=dxdt=−2×10−2×π×sinπtNow, v to be maximum,sinπt should be 1Or, πt=π2∴t=12=0.5sec

The displacement of an object attached to a spring and executing SHM is given by $x = 2 \times 10^{- 2} c o s π τ m$ . In what time the object attains maximum speed first?

$x = 2 \times 10^{- 2} cos π t$
$v = \frac{d x}{d t} = - 2 \times 10^{- 2} \times π \times sin π t$
Now, $v$ to be maximum,
$sin π t$ should be $1$
Or, $π t = \frac{π}{2}$
$∴ t = \frac{1}{2} = 0.5 s e c$