First slide

Simple hormonic motion

Question

The displacement of an object attached to a spring and executing simple harmonic motion is given by $X = 2 Ã 10^{â 2}$ cost $Ït$ metre. The time at which the
maximum speed first occurs is

Easy

A

0.125 s
B

0.25 s
C

0.5 s
D

0.75 s

Solution

given that $X = 2 Ã 10^{â 2} \cos â¡ Ït$
$V = \frac{dx}{dt} = 2 Ï Ã 10^{â 2} \sin â¡ Ït$
The velocity would be maximum when sin $Ït = Â\pm 1$ For first time maximum velocity
$Ït = Ï / 2 or t = \frac{1}{2} = 0 â 5 second .$

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