In an underdamped case, show the values for the constants A and φ in the response function x(t) = Ae^(−ζω_n t) cos(ω_d t + φ)can be calculated from the initial values x_0 and v_0 using A = sqrt( x_0^2 + ( (v_0 + ζω_n x_0)/ ω_d)^ 2 , and φ = tan^−1 [−( v_0 + ζω_n x_0)/ (x_0 w_d)]. Contrast these equations with their analogous equations for an undamped case.