Energy of particle executing SHM depends upon

Options

A. amplitude only
B. Amplitude and frequency
C. velocity only
D. frequency only

Explanation

To solve the question regarding the energy of a particle executing Simple Harmonic Motion (SHM), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Energy in SHM**:
The total mechanical energy (E) of a particle executing 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. **Relating Angular Frequency to Frequency**:
The angular frequency \( \omega \) can be expressed in terms of the frequency \( f \) as:
\[ \omega = 2\pi f \]
Substituting this into the energy equation gives:
\[ E = \frac{1}{2} m (2\pi f)^2 A^2 \]

3. **Expanding the Energy Expression**:
Expanding the equation, we have:
\[ E = \frac{1}{2} m (4\pi^2 f^2) A^2 \]
Simplifying this, we get:
\[ E = 2\pi^2 m f^2 A^2 \]

4. **Identifying Dependencies**:
From the final expression for energy, we can see that the total energy \( E \) depends on:
- The amplitude \( A \) (since \( A^2 \) is present),
- The frequency \( f \) (since \( f^2 \) is present).

5. **Conclusion**:
Therefore, the energy of a particle executing SHM depends on both the amplitude and the frequency. The correct answer is:
- **Option 2: Amplitude and Frequency**.