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 solve the problem, let's break it down step by step.

### Step 1: Understand the relationship between total energy, kinetic energy, and potential energy.
The total mechanical energy (E) of a harmonic oscillator is the sum of its kinetic energy (KE) and potential energy (PE):
\[ E = KE + PE \]

### Step 2: Identify the given values.
From the question, we have:
- Total energy (E) = 9 J
- Potential energy (PE) at the mean position = 5 J

### Step 3: Set up the equation.
Using the relationship from Step 1, we can write:
\[ 9 \, \text{J} = KE + 5 \, \text{J} \]

### Step 4: Solve for kinetic energy (KE).
Rearranging the equation to solve for KE gives:
\[ KE = E - PE \]
Substituting the known values:
\[ KE = 9 \, \text{J} - 5 \, \text{J} \]
\[ KE = 4 \, \text{J} \]

### Step 5: State the final answer.
The kinetic energy at the mean position is:
\[ KE = 4 \, \text{J} \]

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