A body executing `SHM` passes through its equilibrium. At this instant, it has

Options

A. maximum potential energy
B. maximum kinetic energy
C. minimum kinetic energy
D. maximum acceleration

Explanation

To solve the question, "A body executing SHM passes through its equilibrium. At this instant, it has," we will analyze the characteristics of simple harmonic motion (SHM) at the equilibrium position.

### Step-by-Step Solution:

1. **Understanding the Equilibrium Position**:
- In SHM, the equilibrium position is the point where the net force acting on the body is zero. This is also referred to as the mean position.

2. **Potential Energy at Equilibrium**:
- The potential energy (PE) in SHM is given by the formula:
\[ PE = \frac{1}{2} k x^2 \]
where \( k \) is the spring constant and \( x \) is the displacement from the equilibrium position.
- At the equilibrium position, \( x = 0 \). Thus, substituting \( x = 0 \) into the potential energy formula:
\[ PE = \frac{1}{2} k (0)^2 = 0 \]
- This indicates that the potential energy is **minimum** (zero) at the equilibrium position.

3. **Kinetic Energy at Equilibrium**:
- The total mechanical energy (E) in SHM is constant and is the sum of potential energy (PE) and kinetic energy (KE):
\[ E = PE + KE \]
- Since we established that \( PE = 0 \) at the equilibrium position, the total energy is entirely kinetic:
\[ KE = E \]
- The kinetic energy can also be expressed as:
\[ KE = \frac{1}{2} m v^2 \]
- At the equilibrium position, the velocity is at its maximum, which means the kinetic energy is **maximum**.

4. **Acceleration at Equilibrium**:
- The acceleration in SHM is given by:
\[ a = -\omega^2 x \]
where \( \omega \) is the angular frequency and \( x \) is the displacement from the equilibrium position.
- At the equilibrium position, since \( x = 0 \):
\[ a = -\omega^2 (0) = 0 \]
- This indicates that the acceleration is **minimum** (zero) at the equilibrium position.

5. **Conclusion**:
- Therefore, when a body executing SHM passes through its equilibrium position, it has **maximum kinetic energy**, **minimum potential energy**, and **zero acceleration**.

### Final Answer:
At the equilibrium position, the body has **maximum kinetic energy**.