Question

The period of S. H.M. of a particle is 16 second. The phase difference between the positions at $\text{t} = 2\text{ s}$ and $\text{t} = 4\text{ s}$ will be}

• A. $\pi$
• B. $\frac{\pi}{2}$
• C. $\frac{\pi}{4}$
• D. $\frac{\pi}{8}$

Hint:

Phase difference is just the fraction of the total cycle. $2 \text{ s}$ is $1/8$ of the $16 \text{ s}$ period. Since a full cycle is $2\pi$, $1/8$ of $2\pi$ is $\pi/4$.

Answer 1

The Correct Option is C

Step 1: Concept
The phase of a particle in SHM is $\phi = \omega t = \frac{2\pi}{T} t$.

Step 2: Meaning
Phase difference is $\Delta \phi = \frac{2\pi}{T} \Delta t$.

Step 3: Analysis
Given $T = 16 \text{ s}$ and $\Delta t = 4 - 2 = 2 \text{ s}$.
$\Delta \phi = \frac{2\pi}{16} \times 2$
$\Delta \phi = \frac{4\pi}{16} = \frac{\pi}{4}$.

Step 4: Conclusion
The phase difference is $\frac{\pi}{4}$. Final Answer: (C)