The motion of a piston in an automobile engine is nearly simple harmonic. If the 1-kg piston travels back and forth over a total distance of 10.0 cm, what is its maximum speed when the engine is running at 3 000 rpm? The answer is 15.7 m/s but I don't understand how to get there.

Answer 1

displacement=Amax(SIN W T)

VELOCITY= aMAX*W*COS WT

MAX VELOCITY=AMAX*W=.05M*2pi*3000RAD/60
MAX VELOCITY=.05*2pi*50

Answer 2

Maximum speed is w A, where w is the angular velocity and A is the amplitude. The amplitude A is half the displacement of the engine, or 5.0 cm.

The angular velocity in your case is
w = (3000 rev/min)*(2 pi rad/rev)/(60 sec/min) = 314 rad/s

Vmax = 5.0*314 = 1570 cm/s = 15.7 m/s