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Kinetic Energy Formulae

A particle of...

Question

A particle of mass $4 k g$ is executing SHM. Its displacement is given by the equation $y = 8 sin [100 t + \frac{π}{4}] c m$ . Maximum kinetic energy is

128 J

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64 J

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16 v J

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32 J

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Solution

The correct option is A $128 J$
Given,
Mass $m = 4 k g$
$y = 8 s i n [100 t + \frac{π}{4}] . . . . . . . . . . . .1$
Equation of displacement
$y = A s i n (ω t + ϕ) . . . . . . . . . . .2$
Comparing equation 1 and 2 then we get,
$A = 8 c m = 0.08 m$ $ω = 100 r a d / s$
So, maximum $K E = \frac{1}{2} m ω^{2} A^{2} = \frac{1}{2} \times 4 \times 100^{2} \times {0.08}^{2} = 128 J$

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