Final answer:
The amplitude of the motion is 20 cm and the period is 2π/5√3 seconds.
Step-by-step explanation:
In this problem, we are given a mass of 3 kg attached to the end of a spring that is stretched 20 cm by a force of 15 N. The mass is set in motion with an initial position of x(0) = 0 and velocity of v(0) = -10 m/s. We need to find the amplitude and the period of the resulting motion.
The amplitude of the motion can be found using the formula A = x_max - x_eq, where x_max is the maximum displacement and x_eq is the equilibrium position. In this case, the equilibrium position is 20 cm, and the maximum displacement can be found using the initial position x(0) = 0. Therefore, the amplitude is 20 cm.
The period of the motion can be found using the formula T = 2π√(m/k), where m is the mass and k is the force constant of the spring. In this case, m = 3 kg and k = F/x_max = 15 N / 0.2 m = 75 N/m. Plugging in these values, we get T = 2π√(3/75) = 2π/5√3 s. Therefore, the period is 2π/5√3 seconds.