Consider two SHMs along the same straight line $x_1=A_1 \sin \left(\omega t+\phi_1\right)$ and $x_2=A_2 \sin \left(\omega t+\phi_2\right)$,where $A_1$ and $A_2$ are their amplitudes and $\phi_1$ and $\phi_2$ are their initial phase angles. If $R$ is the resultant amplitude,match the conditions in Column-$I$ with the resultant amplitudes in Column-$II$:
Column-$I$ Column-$II$ $A$. $A_1=A_2=A, \delta=0$ $I$. $A_1+A_2$ $B$. $A_1 \neq A_2, \delta=0$ $II$. $0$ $C$. $A_1=A_2=A, \delta=90^{\circ}$ $III$. $2A$ $D$. $A_1=A_2=A, \delta=180^{\circ}$ $IV$. $A\sqrt{2}$
| Column-$I$ | Column-$II$ |
| $A$. $A_1=A_2=A, \delta=0$ | $I$. $A_1+A_2$ |
| $B$. $A_1 \neq A_2, \delta=0$ | $II$. $0$ |
| $C$. $A_1=A_2=A, \delta=90^{\circ}$ | $III$. $2A$ |
| $D$. $A_1=A_2=A, \delta=180^{\circ}$ | $IV$. $A\sqrt{2}$ |
- A$A-IV, B-III, C-II, D-I$
- B$A-III, B-I, C-IV, D-II$
- C$A-I, B-III, C-II, D-IV$
- D$A-III, B-IV, C-I, D-II$
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