#$3(25$ points$)$

The springs and dampers in the system below are governed by the linear constitutive laws $f=kx$ and

$f=bv,k>0,b>0,$ with possibly different $k$ and $b$ for the different elements. The elongated dots are

connections, and they translate only $($they don't tip$/$rotate$).$ The walls are stationary. The elements may in

general be moving. Forces, displacements, and velocities are defined according to our usual positive

conventions. $f_{\text{e}\text{x}\text{t}}$ is an externally applied force. Note that the $f_{\text{e}\text{x}\text{t}}$ arrow pointing to the left means that

$f_{\text{e}\text{x}\text{t}}$ is positive when acting to the left.

$3-1.(12$ pts$)$ Draw the free body diagrams for each of the three connection points $($marked on the figure$),$

indicating the forces acting on it and their direction.

$3-2.($True$/$False; $1$ pts each$)$ For each statement below, mark $"$T$"$ if the statement is true and $"$F$"$ if the

statement is false. A statement is false if it is not necessarily true.

a$),f_5=f_6$

b$),f_5=f_3$

c$),f_1=f_2$

d$)f_6+f_4=f_7$

e$),f_5+f_4=f_7$

f$)f_6+f_4=f_2$

g$),f_5+f_6=f_2$

h$)f_{\text{e}\text{x}\text{t}}+f_1=f_5+f_3$

i$),v_1=v_2$

j$),v_5+v_3=v_7$

k$)v_1+v_2+v_4+v_5+v_6+v_7=0$

l$),v_6=v_4$

m$),v_5+v_6=v_3+v_4$