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If the displacement x and velocity (v) of a particle executing simple harmonic motion are related through the expression 9v2=36−x2, here x is in meter and V is in m/s. Then time period of vibration is

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a

4.5 π sec

b

8π3sec

c

4π sec

d

6π sec

answer is D.

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Detailed Solution

9V2=36−x2⇒V=1362−x2Comparing this equation with the standard equation V=ωA2−x2, we can write ω=13rad/s∴ T=2π/ω=2π1/3sec=6π sec
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