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?

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#### Solution 1

Stroke of piston = 2 times the amplitude

Let A = amplitude,stroke = 1 m

`:. => A = 1/2 m`

Angular frequency, ` omega = 200 "rad/min"`

`V_"max" = ?`

We know that the maximum speed of the block when the amplitude is A

`V_"max" = omegaA = 200 xx 1/2 = 100 "m.min"`

`= 100/60 = 5/3 ms6(-1)= 1.67 ms^(-1)`

#### Solution 2

Angular frequency of the piston, ω = 200 rad/ min.

Stroke = 1.0 m

Amplitude, `A = 1.0/ 2= 0.5 m`

The maximum speed (*v*_{max}) of the piston is give by the relation:

`V_"max" = Aomega`

`= 200 xx 0.5 = 100 "m/min"`

Concept: Periodic and Oscillatory Motions

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