When a body is undergoing undamped vibration, the physical quantity that remains constant is

Options

A. amplitude
B. velocity
C. acceleration
D. phase

Explanation

To solve the question, "When a body is undergoing undamped vibration, the physical quantity that remains constant is," we can follow these steps:

### Step 1: Understand the Concept of Undamped Vibration
Undamped vibration refers to oscillations that occur in a system without any energy loss due to dissipative forces like friction or air resistance. In such a system, the energy remains constant throughout the motion.

**Hint:** Consider what happens to the energy in a system when there are no dissipative forces acting on it.

### Step 2: Identify the Key Characteristics of Undamped Vibration
In undamped vibrations:
- The total mechanical energy (sum of kinetic and potential energy) remains constant.
- The amplitude of the oscillation does not change over time.
- The velocity and acceleration of the oscillating body vary throughout the motion.

**Hint:** Think about the relationship between kinetic energy and potential energy in oscillatory motion.

### Step 3: Analyze the Energy Transformation
In an undamped system, as the body oscillates:
- At maximum displacement (amplitude), the kinetic energy is zero, and potential energy is at its maximum.
- At the equilibrium position, the potential energy is zero, and kinetic energy is at its maximum.
Despite these transformations, the total mechanical energy remains constant.

**Hint:** Remember that in oscillatory motion, energy shifts between kinetic and potential forms but the total remains unchanged.

### Step 4: Conclude on the Constant Physical Quantity
Since the total mechanical energy is conserved and does not change during undamped vibrations, we can conclude that the physical quantity that remains constant is the amplitude of the oscillation.

**Hint:** Reflect on the definition of amplitude and how it relates to the maximum displacement in oscillatory motion.

### Final Answer:
The physical quantity that remains constant when a body is undergoing undamped vibration is the **amplitude** of the oscillation.