Identify the correct statements for an SHM with amplitude A and maximum velocity = V
(i)At position x = $\frac{A}{2}$ , velocity lags displacement by $\frac{π}{2}$
(ii)At position x = $\frac{A}{\sqrt{2}}$ , velocity leads displacement by $\frac{π}{4}$
(iii)When velocity = $\frac{V}{\sqrt{2}}$ , acceleration leads velocity by $π$
(iv)When velocity = $- \frac{V}{\sqrt{2}}$ , acceleration leads velocity by $\frac{π}{2}$

Question

Identify the correct statements for an SHM with amplitude A and maximum velocity = V

(i)At position x = $\frac{A}{2}$ , velocity lags displacement by $\frac{π}{2}$

(ii)At position x = $\frac{A}{\sqrt{2}}$ , velocity leads displacement by $\frac{π}{4}$

(iii)When velocity = $\frac{V}{\sqrt{2}}$ , acceleration leads velocity by $π$

(iv)When velocity = $- \frac{V}{\sqrt{2}}$ , acceleration leads velocity by $\frac{π}{2}$

Infinity Learn · Accepted Answer

In Simple Harmonic Motion, displacement $$y=Asin$$ wt differentiate wrt time t   Velocity,$$v=$$ Awcos $$wt=A$$ wsin $$($$ω$$t+$$π$$2)$$ differentiate wrt time t  and acceleration,$$a=$$–$$Aw2sin$$ $$wt=Aw2sin(wt+$$ π$$)$$         Velocity leads displacement by π$$2$$, acceleration leads velocity by π$$2$$

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