A particle executing a linear SHM has velocities of 8 m/s 7 m/s and 4 m/s, respectively at three points at distances of x m, (x+1) m and (x+2)m from the mean position. What is the maximum velocity of the particle ?

Explanation

To solve the problem step by step, we will use the relationship between the velocity of a particle in Simple Harmonic Motion (SHM) and its position.

### Step 1: Understand the relationship between velocity and position in SHM
In SHM, the velocity \( v \) at a distance \( x \) from the mean position is given by the formula:
\[ v = \sqrt{V_0^2 - \omega^2 x^2} \]
where \( V_0 \) is the maximum velocity, \( \omega \) is the angular frequency, and \( x \) is the displacement from the mean position.
...