Initials: 1. (10 points) question[10] For a), b), c), d) and e) write "True" if the statement is true, or "False" if the statement is false. You must write the full word True or False to receive credit. a) If the solution x(t) of the ODE below represents the position of a mass on a spring, then the mass will oscillate forever, farther from equilibrium each time x" x = cos(3t) = b) If the solution x(t) of the ODE below represents the position of a mass on a spring, then the mass will oscillate forever, farther from equilibrium each time x" +6x= 3 cos(6t) c) If the solution x(t), given below, of a 2nd order, linear, non-homogeneous ODE, represents the position of a mass on a spring, then resonance will occur x(t) = 2 cos(4t) 3 cos(8t) d) If the solution x(t) of the ODE below represents the position of a mass on a spring, then the mass will pass through the equilibrium position infinitely many times, x" 9x+8x= 0 e) If the solution x(t) of the ODE below represents the position of a mass on a spring, and if it begins moving from the equilibrium position x(0) = 0, then no matter what the initial velocity is, the very next time the mass will pass through the equilibrium position is at t = 1. x" +x x = 0 Page 3 of 18 ZOOM +