The energy of a simple harmonic oscillator in the state of rest is 3 Joules. If its mean K.E. is 4 joules, its total energy will be :

Options

A. 7J
B. 8J
C. 10J
D. 11J

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the given information
- The energy of the simple harmonic oscillator in the state of rest (potential energy at maximum displacement) is given as 3 Joules.
- The mean kinetic energy is given as 4 Joules.

### Step 2: Determine the kinetic energy at the mean position
In simple harmonic motion, the total energy (E) is the sum of kinetic energy (KE) and potential energy (PE). At the mean position, the potential energy is zero, and all the energy is kinetic.

The mean kinetic energy is given as 4 Joules. The kinetic energy at the mean position (E2) is twice the mean kinetic energy:
\[ E2 = 2 \times \text{Mean K.E.} = 2 \times 4 \text{ Joules} = 8 \text{ Joules} \]

### Step 3: Calculate the total energy
The total energy (E) of the simple harmonic oscillator is the sum of the potential energy when at rest (E1) and the kinetic energy at the mean position (E2):
\[ E = E1 + E2 \]
Where:
- \( E1 = 3 \text{ Joules} \) (energy in the state of rest)
- \( E2 = 8 \text{ Joules} \) (kinetic energy at the mean position)

Now substituting the values:
\[ E = 3 \text{ Joules} + 8 \text{ Joules} = 11 \text{ Joules} \]

### Final Answer
The total energy of the simple harmonic oscillator is **11 Joules**.

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