First slide

Simple harmonic motion

Question

Identify the correct statements for an SHM
(i) Displacement leads velocity by 0.5 $π$
(ii) Displacement lags velocity by $π$
(iii) Acceleration leads velocity by 0.5 $π$
(iv) Acceleration lags velocity by 0.5 $π$

Easy

A

(i)
B

(iii)
C

(i) and (iii)
D

(ii) and (iv)

Solution

$In SHM, y = Asin ω t ∴ Velocity, v = A ω \cos ω t = A ω \sin (ω t + \frac{π}{2})$
and acceleration, $a = - A ω^{2} \sin ω t = A ω^{2} \sin (ω t + π)$
Velocity leads displacement by $0.5 π$ , acceleration leads velocity by $0.5 π$ .

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