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Q.

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 Simple Harmonic Motion, displacement y=Asin wt differentiate wrt time t Velocity,v= Awcos wt=A wsin (ωt+π2) differentiate wrt time t and acceleration,a=–Aw2sin wt=Aw2sin(wt+ 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