Answer:
Part(a): The equation of motion is .
Part(b): The equation of motion is .
Explanation:
If '' be the mass of the object, '' be the force constant and '' be the damping constant, then the equation of motion of the particle can be written as
Given = 1 Kg, = 14 , = 9. Substituting these values in equation (I),
Taking a trial solution , the auxiliary equation can be written as
and its solutions are , resulting the general solution
The velocity at any instant of time of the mass is
Part(a):
Given . Substituting these values in equation (III) and (IV),
Solving equations (V) and (VI), we have
So the equation of motion is
Part(b):
Given . Substituting these values in equation (III) and (IV),
Solving equations (V) and (VI), we have
So the equation of motion is