P16_003.PDF

3. (a) The motion repeats every 0 . 500s so the period must be T =0 . 500s.

(b) The frequency is the reciprocal of the period: f =1 /T =1 / (0 . 500s) = 2 . 00Hz.

(d) The angular frequency is related to the spring constant k and the mass m by ω = k/m .Wesolve

for k : k = mω 2 =(0 . 500kg)(12 . 57rad / s) 2 =79 . 0N / m.

(e) Let x m be the amplitude. The maximum speed is v m = ωx m =(12 . 57rad / s)(0 . 350m) = 4 . 40m / s.

(f) The maximum force is exerted when the displacement is a maximum and its magnitude is given by

F m = kx m =(79 . 0N / m)(0 . 350m) = 27 . 6N.