The motion of a torsional pendulum is

Options

A. periodic
B. oscillatory
C. simple harmonic
D. angular simple harmonic

Answer

To determine the type of motion exhibited by a torsional pendulum, we can analyze the characteristics of its movement step by step.

### Step-by-Step Solution:

1. **Understanding Torsional Pendulum**:
- A torsional pendulum consists of a disc suspended by a wire (torsional wire). When the disc is twisted and released, it oscillates back and forth around its equilibrium position.

**Hint**: Identify the components of the torsional pendulum and their roles in the motion.

2. **Identifying the Motion**:
- The motion of the disc involves rotating in one direction (e.g., clockwise), coming to rest, then rotating in the opposite direction (e.g., anti-clockwise), and again coming to rest. This pattern repeats over time.

**Hint**: Observe the pattern of motion and note how it returns to a rest position.

3. **Classifying the Motion**:
- Since the motion is repetitive and occurs over a fixed time interval, it is classified as **periodic motion**.

**Hint**: Look for characteristics that define periodic motion, such as repetition over time.

4. **Oscillatory Motion**:
- The motion of the disc can also be described as oscillatory because it moves back and forth around a fixed point (the equilibrium position).

**Hint**: Determine if the motion involves a return to a central position after displacement.

5. **Simple Harmonic Motion (SHM)**:
- Simple harmonic motion is a specific type of oscillatory motion that occurs along a straight line and is characterized by a restoring force proportional to the displacement. Since the torsional pendulum moves in angles rather than along a straight line, it does not qualify as simple harmonic motion.

**Hint**: Recall the definition of SHM and check if the motion adheres to its criteria.

6. **Angular Simple Harmonic Motion**:
- However, since the torsional pendulum exhibits oscillatory motion in angular displacement, it can be classified as **angular simple harmonic motion**.

**Hint**: Consider how angular motion can still be a form of harmonic motion, despite not being linear.

### Conclusion:
Based on the analysis:
- The motion of a torsional pendulum is **periodic** (Option 1), **oscillatory** (Option 2), and **angular simple harmonic motion** (Option 4).
- It is **not** simple harmonic motion in the traditional sense (Option 3).

Thus, the correct options are 1, 2, and 4.