Question

For a particle executing simple harmonic motion, match the following statements (conditions) from column I to statements (shapes of graph) in column II. \begin{center} \includegraphics[]{92.png} \end{center}

• A. a-iv, \quad b-i, \quad c-ii, \quad d-iii
• B. a-iii, \quad b-i, \quad c-ii, \quad d-iv
• C. a-iii, \quad b-ii, \quad c-i, \quad d-iv
• D. a-iv, \quad b-ii, \quad c-i, \quad d-iii

Hint:

For SHM, remember:
- Velocity vs. displacement: Circle
- Acceleration vs. displacement: Straight line
- Acceleration vs. time: Sinusoidal
- Acceleration vs. velocity (if \(\omega \neq 1\)): Ellipse

Answer 1

The Correct Option is B

- The velocity-displacement graph of SHM forms a circle (\( a-iii \)).
- The acceleration-displacement graph is a straight line, as acceleration is directly proportional to displacement (\( b-i \)).
- The acceleration-time graph follows a sinusoidal shape since acceleration varies periodically (\( c-ii \)).
- The acceleration-velocity graph forms an ellipse when \( \omega \neq 1 \) (\( d-iv \)).