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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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