Which of the following statements is correct?

Options

A. Every periodic motion is simple harmonic motion.
B. In simple harmonic motion the period is proportional to the square of the amplitude of oscillation.
C. In simple harmonic motion the phase constant depends on initial condition
D. The resonance frequency of a driven oscillator depends on the damping.

Explanation

To determine which of the statements is correct, let's analyze each statement one by one:

1. **Statement 1**: "Every periodic motion is a simple harmonic motion."
- This statement is **incorrect**. While every simple harmonic motion (SHM) is periodic, not every periodic motion is SHM. For example, the motion of a pendulum is periodic but not necessarily simple harmonic if the angle is large.

2. **Statement 2**: "In a simple harmonic motion, the period is proportional to the square of the amplitude of oscillation."
- This statement is also **incorrect**. In SHM, the period (T) is independent of the amplitude (A). The period is given by \( T = 2\pi\sqrt{\frac{m}{k}} \) for a mass-spring system, where \( m \) is mass and \( k \) is the spring constant. Thus, it does not depend on the amplitude.

3. **Statement 3**: "In simple harmonic motion, the phase constant depends on initial conditions."
- This statement is **correct**. The phase constant (φ) in SHM is determined by the initial conditions of the system, such as the initial position and velocity.

4. **Statement 4**: "The resonance frequency of the driven oscillator depends on the damping."
- This statement is **incorrect**. The resonance frequency of a driven oscillator is primarily determined by the natural frequency of the system and does not depend on the damping. Damping affects the amplitude of oscillation at resonance but not the frequency itself.

Based on this analysis, the correct statement is **Statement 3**: "In simple harmonic motion, the phase constant depends on initial conditions."