The piston in the cylinder head of a locomotive has a stroke of 76.5 cm. What is the maximum speed of the piston if the drive wheels make 193 rev/min and the piston moves with simple harmonic motion?

Here the maximum amplitude of the oscillation, x_m = (76.5 /2) cm
= 38.25 cm
= (38.25 cm) (1 m/100 cm)
= 0.3825 m
Since the drive wheel makes 193 rev/min, therefore angular frequency
w= (193 rev/min) (2π rad/rev) (1 min/60 s)
= 20.2 rad/s
To obtain the maximum speed (v_x) of the piston, substitute 0.3825 m for maximum amplitude of the oscillation x_m and 20.2 rad/s for the angular frequency w in the equation v_x = wx_m,
v_x = wx_m
= (20.2 rad/s) (0.3825 m)
= 7.73 m/s
From the above observation we conclude that, the maximum speed (v_x) of the piston would be 7.73 m/s.