Select wrong statement about simple harmonic motion

Options

A. The body is uniformly accelerated
B. The velocity of the body changes smoothly at all instants
C. The amplitude of oscillation is symmetric about the equilibirum position
D. The frequency of oscillation is independent of amplitude

Explanation

To solve the question of selecting the wrong statement about simple harmonic motion (SHM), we will analyze each statement provided in the question step by step.

### Step 1: Analyze the First Statement
**Statement:** "Body is uniformly accelerated."

- In SHM, the acceleration \( a \) is given by the formula:
\[ a = -\omega^2 x \]
where \( \omega \) is the angular frequency and \( x \) is the displacement from the equilibrium position.
- This equation shows that the acceleration is proportional to the displacement and is directed towards the equilibrium position. Since the acceleration depends on \( x \), it varies as the body moves, indicating that it is not uniform.

**Conclusion:** This statement is **wrong**.

### Step 2: Analyze the Second Statement
**Statement:** "The velocity of the body smoothly changes at all instants."

- The velocity \( v \) in SHM is given by:
\[ v = A \omega \cos(\omega t) \]
where \( A \) is the amplitude.
- The cosine function varies smoothly over time, indicating that the velocity changes continuously and smoothly as the body oscillates.

**Conclusion:** This statement is **correct**.

### Step 3: Analyze the Third Statement
**Statement:** "The amplitude of the oscillation is symmetrically about the equilibrium position."

- The amplitude \( A \) represents the maximum displacement from the equilibrium position. In SHM, the oscillation occurs equally in both directions from the equilibrium position (i.e., \( +A \) and \( -A \)).

**Conclusion:** This statement is **correct**.

### Step 4: Analyze the Fourth Statement
**Statement:** "The frequency of the oscillation is independent of amplitude."

- The frequency \( f \) in SHM is given by:
\[ f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]
where \( k \) is the spring constant and \( m \) is the mass. This equation shows that the frequency depends only on \( k \) and \( m \), and not on the amplitude \( A \).

**Conclusion:** This statement is **correct**.

### Final Conclusion
After analyzing all the statements, we find that the first statement is the only one that is incorrect. Therefore, the answer to the question is:

**Answer:** The first statement "Body is uniformly accelerated" is the wrong statement about simple harmonic motion.

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