7. A particle P, of mass m, is attached to one end of a light elastic spring of natural length a and modulus of elasticity kmg. The other end of the spring is attached to a fixed point O on a ceiling. The point A is vertically below O such that OA = 3a The point B is vertically below O such that OB = a The particle is held at rest at A, then released and first comes to instantaneous rest at the point B. (a) Show that k = (3) (b) Find, in terms of g, the acceleration of P immediately after it is released from rest at A. (3) (c) Find, in terms of g and a, the maximum speed attained by P as it moves from A to B. (6) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________