Now here we are given a piston in the cylinder head of a locomotive, the piston moves with simple harmonic motion and the stroke, or distance between two extremes of the piston is 1m

As shown in figure

Now the stroke is twice the amplitude of the simple harmonic motion so the amplitude is

A = 1/2 m = 0.5 m

Now were are given angular frequency of oscillation

ω = 200 rad/min

we know for a body undergoing simple harmonic motion the velocity is maximum when the body is at mean position or middle position and maximum velocity is given by relation

V = Aω

Where A is the amplitude and ω is the angular frequency of oscillation

So we get maximum velocity of piston as

V = 0.5m × 200rad/min

= 100 m/min

Now 1 minute = 60 second

So we have

V = 100m/60s = 1.67 m/s

So we get maximum velocity of the piston is 1.67 m/s