The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?

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

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