A system like Fig. 13.5 has m = 1 kg and an equation of motion x = 20 cos(8πt −π/4) mm.

Determine:

(a) spring constant k;

(b) static deflection δst;

(c) period;

(d) frequency in hertz; and

(e) velocity, acceleration, and spring force at t = 0.20 s. Plot a phase diagram to scale showing the displacement, velocity, acceleration, and spring-force phasors at this instant.