damped harmonic motion

Question

Two mass-spring systems are experiencing damped harmonic motion, both at 0.7 cycles per second and both with an initial maximum displacement of 12 cm. The first has a damping constant of 0.6, and the second has a damping constant of 0.2. a. Find functions of the form to model the motion in each case. b. How do they differ? (Hint: graph the two functions)

Answer 1

omega = 2pi*0.7 = 4.398, A=12 cm, c₁=0.6, c₂=0.2

x₁(t)=12e^(0.6t)sin(4.398t)

x₂(t)=12e^(0.2t)sin(4.398t)

How do they differ? (Hint: graph the two functions) :

You should graph these functions using your TI calculator and then answer this question.