8 Suppose you have a rock of mass 1 kilogram attached to a s

8) Suppose you have a rock of mass 1 kilogram attached to a spring that stretches 2 meters if you pull on it with a force of 4 newtons. Suppose its damping constant is 1 newton per meter/second.

a. What differential equation does its position x(t) obey?

b. What is the general solution of this equation?

c. Suppose the rock has initial position x(0) = 0 and initial velocity x\'(0) = 1. What is its position at time t = 2?

d. Suppose we also apply an extra force Fextra(t) = sin t. What is the differential equation does x(t) obey now?

e. What is the general solution of this equation?

Solution

m = 1 kilogram, x = 2 meters, F = 4 newtons.

b = damping constant = 1 newton per meter/second.

Hooke