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 relationship with certain quantities, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Energy in SHM**:
The total energy (E) of a particle in simple harmonic motion is given by the formula:
\[ E = \frac{1}{2} k A^2 \]
where \( k \) is the spring constant and \( A \) is the amplitude of the motion.

2. **Relate Total Energy to Amplitude**:
From the formula, we can see that the total energy \( E \) is directly proportional to the square of the amplitude \( A \):
\[ E \propto A^2 \]
This indicates that if the amplitude increases, the total energy increases with the square of that increase.

3. **Consider Other Options**:
- **Acceleration**: The acceleration in SHM is given by \( a = -\omega^2 x \), where \( x \) is the displacement. The total energy does not depend directly on acceleration.
- **Time Period**: The time period \( T \) is related to the angular frequency by \( T = \frac{2\pi}{\omega} \). The total energy does not depend directly on the time period.
- **Mass**: While mass does appear in the total energy formula, it is not squared in relation to energy; thus, it does not fit the requirement of being proportional to the square of a quantity.

4. **Conclusion**:
Since the total energy is directly proportional to the square of the amplitude, the correct answer is:
\[ \text{Total energy is directly proportional to } A^2. \]

### Final Answer:
The total energy of a particle executing SHM is directly proportional to the square of the amplitude (A).

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