A particle undergoes simple harmonic motion having time-period T. The time taken 3/8th oscillation is-

1. Break Down the Problem

We need to find the time taken for $\frac{3}{8}$ of an oscillation of a particle undergoing simple harmonic motion (SHM) with a time period $T$.

2. Relevant Concepts

The time period $T$ is the time taken for one complete oscillation. To find the time for any fraction of the oscillation, we can use the relationship: $\text{Time for } \frac{x}{T} = \frac{x}{1} \cdot T$ where $x$ is the fraction of the oscillation.

3. Analysis and Detail

In our case, we need to calculate the time for $\frac{3}{8}$ of the oscillation. Therefore: $\text{Time taken for } \frac{3}{8} \text{ oscillation} = \frac{3}{8} \cdot T$

4. Verify and Summarize

Now, substituting the value into the formula gives us the required time for $\frac{3}{8}$ of an oscillation.

Final Answer

The time taken for $\frac{3}{8}$ of the oscillation is $\frac{3T}{8}$.