My Report 1 Problem (1.2)
From Newton's Second Law and summing forces in the y-direction:
Where is the force due to the spring, is the force due to the dashpot, and is the applied force.
Both the force due to the spring and the force due to the dashpot oppose motion, and is assumed to act in the negative y direction.
My Report 2 problem (2.8)
Writing the characteristic equation:
Which is now in the form:
Solving for the two roots:
We will find the discriminant to be less than 0, leading to complex conjugate roots:
Which leads to a solution of the form:
Where , therefore:
Giving us a solution of: