The graph plotted between phase angle ((φ)) and displacement of a...

Key Relationships in SHM: 1. Displacement $y$ vs. Phase Angle (\phi) : The displacement from the equilibrium position varies sinusoidally with respect to time and phase angle. 2. Kinetic Energy (K.E.): - K.E. is maximum when the displacement is zero (i.e., at the mean position). - It varies sinusoidally and reaches zero at the maximum displacements (($\pm$) A). - K.E. vs. Phase Angle: This will be a cosine-like curve because it is maximum at (\phi=0) and (\phi=$\pi$) (mean position) and zero at (\phi=$\frac{\pi}{2}$) and ($\frac{3 \pi}{2}$) (maximum displacements). 3. Potential Energy (P.E.): - P.E. is maximum when the displacement is maximum (($\pm \mathrm{A}$)) and zero at the mean position. - P.E. vs. Phase Angle: This will also be a cosine-like curve that is maximum at (\phi=$\frac{\pi}{2}$) and ($\frac{3 \pi}{2}$) (maximum displacements) and zero at (\phi=0) and (\phi=$\pi$) (mean position). 4. Total Energy (T.E.): - T.E. remains constant in SHM and is equal to the maximum potential or kinetic energy. - T.E. vs. Phase Angle: This is a constant line across all phase angles. 5. Velocity: - Velocity is maximum when displacement is zero (mean position) and zero when displacement is maximum. - Velocity vs. Phase Angle: This will be a sine wave, starting from zero at (\phi=0) and reaching maximum at (\phi=$\frac{\pi}{2}$). Matching the Columns: - (a) K.E. versus phase angle: Matches with (ii) (cosine curve). (b) P.E. versus phase angle: Matches with (i) (also cosine curve, but maximum at extremes). (c) T.E. versus phase angle: Matches with (iv) (constant value). - (d) Velocity versus phase angle: Matches with (iii) (sine wave).