What is constant in SHM ?

Options

A. Restoring force
B. kinetic energy
C. Potential energy
D. Periodic time

Explanation

To determine what remains constant in Simple Harmonic Motion (SHM), we can analyze each of the given options step by step:

### Step 1: Analyzing the Restoring Force
The restoring force in SHM is given by the formula:
\[ F = -kx \]
where \( k \) is the spring constant and \( x \) is the displacement from the mean position. Since this force depends on the displacement \( x \), it changes as the object moves. Therefore, the restoring force is **not constant**.

**Hint:** Remember that the restoring force varies with displacement in SHM.

### Step 2: Analyzing Kinetic Energy
The kinetic energy (KE) of an object in SHM can be expressed as:
\[ KE = \frac{1}{2} k (A^2 - x^2) \]
where \( A \) is the amplitude and \( x \) is the displacement. Since the kinetic energy depends on the displacement \( x \), it also changes as the object moves. Thus, kinetic energy is **not constant**.

**Hint:** Kinetic energy depends on the position of the object in its motion.

### Step 3: Analyzing Potential Energy
The potential energy (PE) in SHM is given by:
\[ PE = \frac{1}{2} k x^2 \]
Again, this depends on the displacement \( x \). As the object moves, the potential energy changes with the square of the displacement. Therefore, potential energy is also **not constant**.

**Hint:** Potential energy varies with the square of the displacement in SHM.

### Step 4: Analyzing Periodic Motion
The time period \( T \) of SHM is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass of the object and \( k \) is the spring constant. The time period is independent of the amplitude and displacement. It remains constant throughout the motion, meaning the time taken for one complete cycle is always the same.

**Hint:** The time period is a characteristic of the motion and does not change with position or time.

### Conclusion
From the analysis, we find that the only quantity that remains constant in Simple Harmonic Motion is the **time period** of the motion. Therefore, the correct answer is:

**The time period of the motion is constant in SHM.**