A particle moves on the x axis attracted toward the origin O on it with a force proportional to its instantaneous distance from O. If it starts from rest at x = 5 cm and reaches x = 2.5 cm for the first time after 2 s, find

(a) The position at any time t after it starts,

(b) The speed at x = 0,

(c) The amplitude, period and frequency of the vibration,

(d) The maximum acceleration,

(e) The maximum speed.