We know that a particle performs a SHM and that at instant t1 = 10 s its position, velocity and acceleration are respectively equal to x1 = −5.8438 mm, v1 = 61.199 mm/s and a1 = 11834 mm/s 2 . 

Determine: 

(a) What is the period of the motion? 

(b) Find the equation x(t) of motion. 

(c) At what time t2, immediately after 20 s, will it be back at x1 with speed v1. 

(d) Answer the previous question but without requiring now that the velocity is necessarily v1.