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
