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*Question:* A piston in a stream engine executes simple harmonic motion.
Given that the maximum displacement of the piston from its centre-line is
,
and that the mass of the piston is , find the maximum velocity of the piston
when the steam engine is running at 4000rev./min. What is the maximum acceleration?
*Answer:* We are told that the amplitude of the oscillation is
.
Moreover, when converted to cycles per second (*i.e.*, hertz), the frequency of the oscillation becomes

Hence, the angular frequency is

Consulting Tab. 4, we note that the maximum velocity of an object executing
simple harmonic motion is
. Hence, the maximum velocity is

Likewise, according to Tab. 4, the maximum acceleration is given by

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Richard Fitzpatrick
2006-02-02