User:Egm4313.s12.team20.eizagaechevarria/Report 1

Given
Free body diagram:



Solution
By definition:

$$\displaystyle a=y'' $$

(3.1)

$$\displaystyle f_k=ky_k$$ (3.2)

$$\displaystyle f_c=cy_c' $$ (3.3)

Since the spring, dashpot and mass are aligned, the forces on the dashpot are equal and opposite and can be described as the internal forces.

$$ \displaystyle f_k=f_c=f_I $$ (3.4)

The net force of the system is the difference between the applied force and the internal force.

$$ \displaystyle F_s=f(t)-f_I $$ (3.5)

Applying Newtons 2nd law:

$$\displaystyle F_s=m*a $$  (3.6)

Plug in equation (3.1) and (3.5) into equation (3.6):

$$\displaystyle

my''=f(t)-f_I $$  (3.7)

Rearrange: