Amass m = 0.85 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. the spring has spring constant k = 65 n/m and negligible mass. at time t = 0 the mass is released from rest at a distance d = 0.45 m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y(t) = a cos(ωt – φ). the positive y-axis points upward.

(a) find the angular frequency of the oscillation, in radians per second.
( b) determine the value of φ, in radians.
(c) calculate coefficient a, in meters.
(d) what is the mass’s velocity along the y-axis, in meters per second, at time t1 = 0.15 s?
(e) what is the magnitude of the mass’s maximum acceleration, in meters per second squared?
(f) what is the magnitude of the mass s maximum acceleration, in meters per second squared?