The total energy of a particle executing SHM is directly proportional to the square of the following quantity.

Options

A. Acceleration
B. Amplitude
C. Time period
D. Mass

Explanation

To solve the question regarding the total energy of a particle executing Simple Harmonic Motion (SHM) and its proportionality to the square of a certain quantity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Energy in SHM**:
The total energy (E) of a particle in SHM is given by the formula:
\[ E = \frac{1}{2} m \omega^2 A^2 \]
where:
- \( m \) is the mass of the particle,
- \( \omega \) is the angular frequency,
- \( A \) is the amplitude of the motion.

2. **Identify the Proportionality**:
From the formula, we can see that the total energy \( E \) is directly proportional to \( \omega^2 \) and \( A^2 \). This means:
\[ E \propto \omega^2 \quad \text{and} \quad E \propto A^2 \]

3. **Conclusion**:
Since the question asks for the quantity to which the total energy is directly proportional to the square of, we can conclude that:
- The total energy is directly proportional to the square of the amplitude \( A \) and the square of the angular frequency \( \omega \).

4. **Final Answer**:
Therefore, the total energy of a particle executing SHM is directly proportional to the square of the amplitude \( A \) and the square of the angular frequency \( \omega \).