In each of the questions below, hanging a mass m from a spring stretches the spring l meters from its unloaded length. calculate the spring constant k, write the differential equation that governs the motion of the undamped mass-spring system, and find the solution that satisfies the initial conditions specified. units are mks; gravitational constant is 9.8 m/s m-0.2 kg and1.0889meters initial displacement is 0.4 and initial velocity is 0.7 k1.8 kg/s2 0.4 cos(4.24 t)0.4000 sin(4.24t) m 0.3 kg and l-2.4500 meters initial displacement is 0.5 and initial velocity is 0.4 k12 kg/s2 x"+0.5x xt)0.5 cos(0.5 t) 0.4000 sin (0.5 t) m=0.5 kg and l=0.6125 meters initial displacement is 0.9 and initial velocity is 0.9 k=8 x(t) = 0.9 . cos ( 8 t) + 0.4000 . sin ( 8 t)