Identify the correct statements for an SHM with amplitude A and maximum velocity = V(i)At position x = A2, velocity lags displacement by π2(ii)At position x = A2, velocity leads displacement by π4(iii)When velocity = V2, acceleration leads velocity by π(iv)When velocity = −V2, acceleration leads velocity by π2
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a
(i) only
b
(iii) only
c
(i) and (iii) only
d
(iv) only
answer is D.
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Detailed Solution
In SHM, y=Asinωt ∴ Velocity, v=Aωcosωt=Aωsinωt+π2and acceleration, a=−Aω2sinωt=Aω2sin(ωt+π)Velocity leads displacement by π2 , acceleration leads velocity by π2.
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Identify the correct statements for an SHM with amplitude A and maximum velocity = V(i)At position x = A2, velocity lags displacement by π2(ii)At position x = A2, velocity leads displacement by π4(iii)When velocity = V2, acceleration leads velocity by π(iv)When velocity = −V2, acceleration leads velocity by π2