The total energy of a harmonic oscillator of mass 2 kg is 9 J. If its potential energy at mean position is 5 J , its KE at the mean position will be

Options

A. 9 J
B. 14 J
C. 4 J
D. 11 J

Explanation

To find the kinetic energy (KE) at the mean position of a harmonic oscillator, we can use the relationship between total energy (TE), kinetic energy (KE), and potential energy (PE). The total energy of a harmonic oscillator is the sum of its kinetic and potential energy.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Total Energy (TE) = 9 J
- Potential Energy (PE) at the mean position = 5 J

2. **Use the Energy Relationship:**
The relationship between total energy, kinetic energy, and potential energy is given by the equation:
\[ \text{TE} = \text{KE} + \text{PE} \]

3. **Substitute the Known Values:**
We can rearrange the equation to solve for kinetic energy:
\[ \text{KE} = \text{TE} - \text{PE} \]
Substituting the known values:
\[ \text{KE} = 9 \, \text{J} - 5 \, \text{J} \]

4. **Calculate the Kinetic Energy:**
\[ \text{KE} = 4 \, \text{J} \]

5. **Conclusion:**
The kinetic energy at the mean position is 4 J.

### Final Answer:
The kinetic energy at the mean position is **4 J**.

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