Answers to question P: a) under-damped b) x(t) = A cos(omega*t + phi) e^(-t/tau) or x(t) = A cos(omega*t) e^(-t/tau) + B cos(omega*t) e^(-t/tau) c) omega = 4.8967 rad/s d) period = 1.2832 s e) using the first form of the general solution, x(t) = (-2.5033 m) cos( [4.8967 rad/s]*t + 0.05101 rad) e^(-t/6.667 s) f) look at the file http://spiff.rit.edu/classes/phys283/prac/prac_t1/prob_p.png or, for a rough sketch, 2.5 +--------------------------------------------------------------------+ | ** + + + + | 2 |-+***.......**.............:............:.............:...........+-| | * * *** * : : : | 1.5 |-+*..*.....*.*......***....:..*.........:.............:...........+-| 1 |-+*..*.....*.**.....*.*....:.***......**:.............:...........+-| | * * * :* * ** : * * *** ** : ** | 0.5 |-**..*....*..:*....*...*...:*..**....**.*.....****....:****.....***-| | * * * :* * * :* * * ** * ** :* * * **| 0 |-*...**...*..:*....*...*...:*...*...**..:*...**...*...**..**...*..+*| | * * * : * * ** ** ** * :** * ** * ** ** | -0.5 |-*....*...*..:.*..*.....*..*.....*..*...:.*.**.....*.*:.....***...+-| | * * * : * * * * * ** : *** ***: | -1 |**....*..*...:.*..*.....****.....***....:..*..........:...........+-| |* ** * : *** **: : : | -1.5 |*+.....*.*...:..**.........:............:.............:...........+-| -2 |*+.....**....:.............:............:.............:...........+-| |* ** : : : : | -2.5 |-+...........:.............:............:.............:...........+-| | + + + + | -3 +--------------------------------------------------------------------+ 0 2 4 6 8 10