The `P.E.` of an oscillation particle at rest position is `10J` and its average `K.E.` is `5J`. The total energy of particle at any instant will be-

Options

A. `10 J`
B. `20 J`
C. `25 J`
D. `5 J`

Explanation

To solve the problem, we need to determine the total energy of an oscillating particle given its potential energy (P.E.) at the rest position and its average kinetic energy (K.E.).

### Step-by-Step Solution:

1. **Identify Given Values**:
- Potential Energy (P.E.) at the rest position = 10 J
- Average Kinetic Energy (K.E.) = 5 J

2. **Understand Energy Conservation in Simple Harmonic Motion**:
- In simple harmonic motion (SHM), the total mechanical energy (E) is conserved. This means that at any point in the oscillation, the total energy is the sum of the potential energy and kinetic energy:
\[ E = P.E. + K.E. \]

3. **Evaluate Total Energy at the Rest Position**:
- At the rest position (equilibrium position), the potential energy is at its maximum, and the kinetic energy is zero. Therefore, the total energy at this position is equal to the potential energy:
\[ E = P.E. = 10 J \]

4. **Conclusion**:
- The total energy of the particle at any instant is constant and is equal to the potential energy at the rest position, which is 10 J.

### Final Answer:
The total energy of the particle at any instant will be **10 J**.

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