Question

1. In an engine, 200 g piston oscillates in simple harmonic motion with displacement

varying according to x(t) = 5 cos 2t where x is in meter and t is in second.

a) Write the expression for its velocity as a function of time

b) Sketch a graph of velocity against time of the piston for the first complete cycle

starting from t = 0.

c) Calculate the maximum acceleration of the system

d) Calculate the total energy of the system

Answer 1

a) $v(t)=-10\sin2t$

b)

c) $a(t)=-20\cos2t\to |a_{max}|=20\ (m/s^2)$

d) $E=m\omega^2A^2/2=0.2\cdot2^2\cdot5^2/2=10\ (J)$