Comparing L-C oscillation with the oscillation if spring-block-system, match the following table.
Comparing L-C oscillations with the oscillations of spring-block sytem, match the following table `{:(,,underset(("LC oscillations"))"Table-1",,underset(("Spring-block oscillations"))"Table-2"),(,(A),L,(P),k),(,(B),C,(Q),m),(,(C),i,(R),v),(,(D),(di)/(dt),(S),x),(,,,(T),"None"):}`

Answer

To solve the problem of matching LC oscillations with spring-block oscillations, we will analyze the equations governing both systems and identify their corresponding parameters.

### Step 1: Understand the equations of motion

For the **spring-block system**, the equation of motion is given by:
\[ m \frac{d^2x}{dt^2} + kx = 0 \]
where:
- \( m \) is the mass of the block,
- \( k \) is the spring constant,
- \( x \) is the displacement.

For **LC oscillations**, the equation of motion is:
\[ L \frac{d^2I}{dt^2} + \frac{1}{C} Q = 0 \]
where:
- \( L \) is the inductance,
- \( C \) is the capacitance,
- \( I \) is the current,
- \( Q \) is the charge.

### Step 2: Identify corresponding parameters

1. **Mass (m) and Inductance (L)**:
- In the spring-block system, \( m \) is the mass.
- In LC oscillations, \( L \) plays a similar role to mass in terms of inertia in the oscillation.
- Therefore, \( m \) corresponds to \( L \).

2. **Spring constant (k) and Capacitance (C)**:
- The spring constant \( k \) in the spring-block system is analogous to the capacitance \( C \) in LC oscillations.
- The relationship can be noted as \( k \sim \frac{1}{C} \).
- Thus, \( k \) corresponds to \( \frac{1}{C} \).

3. **Displacement (x) and Charge (Q)**:
- Displacement \( x \) in the spring-block system corresponds to the charge \( Q \) in LC oscillations.
- Therefore, \( x \) corresponds to \( Q \).

4. **Velocity (v) and Current (i)**:
- The velocity \( v \) in the spring-block system is the rate of change of displacement, \( v = \frac{dx}{dt} \).
- The current \( i \) in LC oscillations is the rate of change of charge, \( i = \frac{dQ}{dt} \).
- Hence, \( v \) corresponds to \( i \).

5. **Acceleration and Rate of Change of Current**:
- The acceleration in the spring-block system is given by \( \frac{d^2x}{dt^2} \).
- In LC oscillations, the rate of change of current can be represented as \( \frac{di}{dt} \).
- Therefore, acceleration corresponds to \( \frac{di}{dt} \).

### Step 3: Match the parameters

Now we can summarize the matches:
- \( A \) (L) matches with \( P \) (k)
- \( B \) (C) matches with \( Q \) (m)
- \( C \) (i) matches with \( R \) (v)
- \( D \) (di/dt) matches with \( S \) (x)

### Final Matching Table

| Table-1 (LC oscillations) | Table-2 (Spring-block oscillations) |
|---------------------------|-------------------------------------|
| A (L) | P (k) |
| B (C) | Q (m) |
| C (i) | R (v) |
| D (di/dt) | S (x) |