Match the following
`{:("List - I","List - II"),("(a) acceleration","(e) A"sin omega t),("(b) time period","(f) A"^(2) omega cos omega t),("(c) displacement","(g) A" omega cos omega t),("(d) velocity","(h) -A" omega^(2) sin omega t),(,"(i) 2"pi sqrt((l)/(g))):}`

Options

A. a - h, b - f, c - e, d - i
B. a - h, b - i, c - e, d - g
C. a - f, b - h, c - g, d - e
D. a - h, b - f, c - e, d - g

Answer

To solve the matching question, we need to identify the correct relationships between the physical quantities in List - I and their corresponding expressions in List - II based on the principles of Simple Harmonic Motion (SHM).

### Step-by-Step Solution:

1. **Identify the expressions for each quantity in SHM**:
- **Displacement (x)**: In SHM, the displacement can be expressed as:
\[ x(t) = A \sin(\omega t) \]
This corresponds to option (e) in List - II.

2. **Determine the expression for velocity (v)**:
- The velocity is the time derivative of displacement:
\[ v(t) = \frac{dx}{dt} = A \omega \cos(\omega t) \]
This corresponds to option (g) in List - II.

3. **Determine the expression for acceleration (a)**:
- The acceleration is the time derivative of velocity:
\[ a(t) = \frac{dv}{dt} = -A \omega^2 \sin(\omega t) \]
This corresponds to option (h) in List - II.

4. **Identify the time period (T)**:
- The time period of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{l}{g}} \]
This corresponds to option (i) in List - II.

5. **Match the quantities from List - I to List - II**:
- (a) Acceleration → (h) \(-A \omega^2 \sin(\omega t)\)
- (b) Time period → (i) \(2\pi \sqrt{\frac{l}{g}}\)
- (c) Displacement → (e) \(A \sin(\omega t)\)
- (d) Velocity → (g) \(A \omega \cos(\omega t)\)

### Final Matching:
- (a) → (h)
- (b) → (i)
- (c) → (e)
- (d) → (g)