Match List-I with List-II.

**List-I (Graphs)**
(a) Displacement-time graph with decreasing amplitude (Damped)

Question

Match List-I with List-II.

**List-I (Graphs)**
(a) Displacement-time graph with decreasing amplitude (Damped)
(b) Displacement-time graph with constant amplitude (Undamped)
(c) Force-displacement graph (Linear relationship, F = -kx)
(d) Energy-time graph (Constant total energy)

**List-II (Situations)**
(i) Total mechanical energy is conserved
(ii) Bob of a pendulum is oscillating under negligible air friction
(iii) Restoring force of a spring
(iv) Bob of a pendulum is oscillating along with air friction

Choose the correct answer from the options given below:

Accepted Answer

1.  **Damped Oscillation (a):** When a pendulum oscillates with air friction (damping force), energy is dissipated, and the amplitude decreases with time. This matches with **(iv)** Bob of a pendulum is oscillating along with air friction .
2.  **Undamped Oscillation (b):** In the absence of friction (negligible air resistance), the amplitude of oscillation remains constant (Ideal SHM). This matches with **(ii)** Bob of a pendulum is oscillating under negligible air friction.
3.  **Restoring Force (c):** For a spring, the restoring force obeys Hooke's Law ($F = -kx$), which implies a linear relationship between Force and Displacement with a negative slope. This matches with **(iii)** Restoring force of a spring .
4.  **Conservation of Energy (d):** In an ideal SHM system (conservative forces only), the total mechanical energy (Kinetic + Potential) remains constant over time. This is represented by a straight horizontal line in an energy-time graph. This matches with **(i)** Total mechanical energy is conserved.
5.  **Conclusion:** The correct matching sequence is (a)-(iv), (b)-(ii), (c)-(iii), (d)-(i).

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