The motion of a piston in an automobile engine is nearly simple harmonic. If the 1-kg piston travels back and forth over a distance of 12.0 cm, what is its maximum speed when the engine is running at 3000 rpm?

Answer 1

3000 rpm is a period of 1/50 second
So, with an amplitude of 6, the function is
y = 6 sin(100π t)
so, the speed is 600π cos(100π t), which has a maximum value of 600π cm/s