A particle is executing SHM along a straight with an amplitude of 5 cm and time period 2 sec. Find the acceleration of the particle when its velocity is equal to half of its maximum velocity.
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a
17.84 cm/s2
b
13.59 cm/s2
c
42.50 cm/s2
d
27.42 cm/s2
answer is B.
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Detailed Solution
Y=ωA2-x2 ⇒x=A2-V2ω2=1ωA2ω2-V2=1ωVm2-V2 ∴Acceleration a=ω2x=ωVm2-V2=ωVm2-Vm22=32Aω ∴a=32x 5 x 10-2 x 2π2m/s2=13.59 cm/s2