Question

The position of a mass tied to a spring hanging from the ceiling is given by x (t), measured in meters and t is measured in seconds. The position = 0 is the "equilibrium position" and positive values represent positions below the equilibrium position. The ODE modeling the position and initial conditions are: x" + 4x = 0, x(0) = 0, x' (0) = -3 Which of the following statements is true about the mass? It starts moving at t= 0 at the equilibrium position, then passes through the equilibrium position every seconds It starts moving at t = 0 at the equilibrium position, then passes through the equilibrium position every seconds It starts moving at t = 0 at the equilibrium position, then passes through the equilibrium position every 2 seconds It never passes through the equilibrium position for t > 0 It starts moving at t = 0) at the equilibrium position, then passes through the equilibrium position every seconds

Answer 1

x"+4x=0 x(0)=0, x'(0)=-3 (DP+4)x=0 D2+4=0 → D=21,-2i X(t)= Acos2t+Bsinat At t=0, x=0 → 0=A+0= A=0 x'(t)=2Bcos2t at t=0 x'(0)=-3 -3=2B → B=-3/2 → X(t)= sin 2t w²4 → w=2 27 - =7 W So it starts moving at t=0, at the eqbm position and passes the eqbm position at every seconds