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Question

A body describing SHM has a maximum acceleration of $8 π$ m/s $^{2}$ and a maximum speed of 1.6 m/s. Find the period T and the amplitude A.

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$ω^{2} A = 8 π$ .............(i)
$ω A = 1.6$ ...............(ii)
Solving these two equations we get
$ω = 5 π$ rad/s
$∴$ $T = \frac{2 π}{ω} = \frac{2 π}{5 π} = 0.4$ s
And $A = \frac{1 . 6}{ω} = \frac{1 . 6}{5 π}$
$= 0.102 m$

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