The energy at the mean position of a pendulum will be

Options

A. zero
B. partial PE and partial KE
C. totally KE
D. totally PE

Explanation

To determine the energy at the mean position of a pendulum, we can analyze the kinetic and potential energy involved in simple harmonic motion (SHM). Here’s a step-by-step solution:

### Step 1: Understand the Energy Forms in SHM
In simple harmonic motion, the total mechanical energy (E) of the system is the sum of kinetic energy (KE) and potential energy (PE). The formulas for these energies are:
- Kinetic Energy (KE) = \( \frac{1}{2} m \omega^2 (A^2 - x^2) \)
- Potential Energy (PE) = \( \frac{1}{2} m \omega^2 x^2 \)

Where:
- \( m \) = mass of the pendulum bob
- \( \omega \) = angular frequency
- \( A \) = amplitude of the motion
- \( x \) = displacement from the mean position

### Step 2: Identify the Mean Position
The mean position of the pendulum corresponds to the point where the displacement \( x = 0 \).

### Step 3: Calculate Kinetic Energy at Mean Position
Substituting \( x = 0 \) into the kinetic energy formula:
\[ KE = \frac{1}{2} m \omega^2 (A^2 - 0^2) = \frac{1}{2} m \omega^2 A^2 \]

### Step 4: Calculate Potential Energy at Mean Position
Substituting \( x = 0 \) into the potential energy formula:
\[ PE = \frac{1}{2} m \omega^2 (0^2) = 0 \]

### Step 5: Determine Total Energy at Mean Position
The total energy at the mean position is entirely kinetic since the potential energy is zero:
\[ E = KE + PE = \frac{1}{2} m \omega^2 A^2 + 0 = \frac{1}{2} m \omega^2 A^2 \]

### Conclusion
At the mean position of a pendulum, the energy is entirely kinetic. Therefore, the answer to the question is that the energy at the mean position of a pendulum will be **totally kinetic energy**.

### Final Answer
The energy at the mean position of a pendulum will be **totally kinetic energy**.

---