A freely vibrating mass-spring-damper system has the following properties: m = 2 kg, k = 6 N/m, c = 1.6 N·s/m. The initial condition is x (0) = 0, x˙ (0) = 0.8. Calculate the damped natural frequency,...

A freely vibrating mass-spring-damper system has the following properties: m = 2 kg, k = 6 N/m, c = 1.6 N·s/m. The initial condition is x (0) = 0, x˙ (0) = 0.8. Calculate the damped natural frequency, amplitude Ad and phase angle φd and calculate the response amplitude at t = 3.5 seconds. Verify your answer by using Equation (6.88).