Question

A body of mass one kg is executing shm its displacement y=6 sin(100t+pi/4) its maximum k.E

Answer 1

Dear friends

In SHM maximum velocity is given by ,vmax= omega.amplitude  

vmax=100 . 6  = 600 cm/s = 6 m/sec

so K.Emax= ½ * 6 *6 = 18 J

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Answer 2

The maximum kinetic energy of the body is 18 Joules.

Explanation:

Given that,

Mass of the body, m = 1 kg

A body of mass 1 kg is executing SHM, its displacement is given by :

$y=6\ sin(100t+\pi/4)$...........(1)

The general equation of SHM is given by :

$y=A\ sin(\omega t+\pi/4)$

The maximum kinetic energy of the body that is executing SHM is given by :

$E=\dfrac{1}{2}mA^2\omega^2$..........(2)

On comparing equation (1) and (2) we get :

$A=6\ cm=0.06\ m$

$\omega=100$

$E=\dfrac{1}{2}\times 1\times 0.06^2\times (100)^2$

E = 18 J

So, the maximum energy of the body is 18 J. Hence, this is the required solution.

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Topic : Simple Harmonic Motion

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