Answer
$\text{ Particle 2 will have the greatest maximum velocity.}$
Work Step by Step
$\text{Let's first find Amplitude and Time period for each graph given:}$
$\text{For the first graph:}$
$A_1 = A$
$\text{Say the time period is }T_1 =T$
$\text{For the second graph:}$
$A_1 = 3A$
$\text{The particle performs three oscillations in time T}$
$\therefore T_2 =\frac{T}{3}$
$\text{For the third graph:}$
$A_1 = 2A$
$\text{The particle performs tow oscillations in time T}$
$\therefore T_2 =\frac{T}{2}$
$\text{Maximum Velocity is given by }v_{max} = A\omega = \frac{A\times 2\pi}{T}$
$$\therefore v_{max}\propto \frac{A}{T}$$
$\text{So higher the A/T ratio, higher the max velocity}$
$\text{For particle 1}$
$$\frac{A_1}{T_1} = \frac{A}{T}$$
$\text{For particle 2}$
$$\frac{A_2}{T_2} = \frac{3A}{\frac{T}{3}} = \frac{9A}{T}$$
$\text{For particle 3}$
$$\frac{A_3}{T_3} = \frac{2A}{\frac{T}{2}} = \frac{4A}{T}$$
$\therefore \text{ Particle 2 will have the greatest maximum velocity.}$
