A wave pulse is travelling along +x direction on a string at `2 m//s`. Displacement y (in cm ) of the parrticle at x=0 at any time t is given by `2//(t^(2)+1)`. Find
(i) expression of the function y=(x,t),i.e., displacement of a particle at position x and time t.
Draw the shape of the pulse at t=0 and t=1 s.

Explanation

To solve the problem, we need to find the expression for the displacement \( y(x, t) \) of a particle on a string at position \( x \) and time \( t \), given the displacement at \( x = 0 \) as \( y(0, t) = \frac{2}{t^2 + 1} \) and the speed of the wave pulse as \( 2 \, \text{m/s} \).

### Step 1: Understand the given data
We know that the wave pulse is traveling in the positive x-direction with a speed of \( v = 2 \, \text{m/s} \). The displacement at \( x = 0 \) is given by the function \( y(0, t) = \frac{2}{t^2 + 1} \).

### Step 2: Relate position and time
The relationship between distance, speed, and time is given by:
\[
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