Answer:
F = - K X force constant for spring
a = F / m maximum acceleration
F = 4.5 kg * 26 m/s^2 = 117 Newtons
(A) K = 117 N / .038 m = 3079 N/m
ω = (K/M)^1/2 = (117/5)^1/2 = 4.84 / sec
(B) f = ω / 2 pi = 4.84 / 6.28 = .77 /sec
(C) P = 1 / f = 1/.77 = 1.30 sec