The piston in a particular car engine moves in approximately simple harmonic motion with an amplitude of 8 cm. The mass of the piston is 8 kg and the piston makes 100 oscillations per second. Calculate:

Question

a) the maximum value if the acceleration of the piston.

b) the force needed to produce this acceleration.

Answer 1

x = .08 sin 2 pi (100)t
= .08 sin 628 t

v = dx/dt = .08(628) cos 628 t

a = d^2x/dt^2 = -.08(628)^2 sin 628 t
so
max a = .08(628^2)
max f = m a = 8 * max a