Question

Consider a damped mass/spring system with spring constant, mass and damping coefficient

being, respectively,

κ = 4 , m = 1 and γ = 5 .

a. Verify that this system is overdamped.

b. Find and roughly graph the position of the object over time, y(t), assuming that y(0) = 2 and y'(0) = 0 .

c. Find and roughly graph the position of the object over time, y(t), assuming that y(0) = 0 and y(0) = 2 .

Answer 1

An overdamped system moves slowly toward equilibrium. An underdamped system moves quickly to equilibrium, but will oscillate about the equilibrium point as it does so. A critically damped system moves as quickly as possible toward equilibrium without oscillating about the equilibrium.

Step-by-step explanation:

An overdamped system moves slowly toward equilibrium. An underdamped system moves quickly to equilibrium, but will oscillate about the equilibrium point as it does so. A critically damped system moves as quickly as possible toward equilibrium without oscillating about the equilibrium.