The motion of a piston in an auto engine is simple harmonic. The piston travels back and forth over a distance of 23 cm, and the piston has a mass of 1.7 kg.

Question

2515 rpm 23 cm
max speed of the piston 30.28757 m/s

What is the maximum force acting on the
piston when the engine is running at the same rate? Answer in units of N

Answer 1

find the frequency in Hz
f = 2515 rev/min (1 min/60 s) = 41.92 Hz

y = (0.23/2)sin (2 pi f t)
y = 0.115 sin 263 t
v = (0.115)(263) cos 263 t so yes max of 30.29 m/s
a = -30.29(263)sin 263 t
so max a = 7966 m/s^2
F = m a = 1.7*7966 = 13543 Newtons

Answer 2

thank you!!!!!
i must have messed up on my calculations