Question $6$

For a mass$-$spring$-$damper system the governing equation is:

mx$^()+$cx$^()+$kx$=$F$($t$)$

m$=7$kg

c$=4$N$^(*)($s$)/($m$)$

k$=48($N$)/($m$)$

F$($t$)=0\mathrm{.}6$N

Determine the position, using

x$.$xxx format, at t$=3$sec if the system starts

from x$(0)=$x$\_($o$)=0\mathrm{.}2$m with an initial velocity of $0($m$)/($s$)$

Question $7$

For a mass$-$spring$-$damper system the governing equation is:

mx$^()+$cx$^()+$kx$=$F$($t$)$

m$=5$kg

c$=1$N$^(*)($s$)/($m$)$

k$=3($N$)/($m$)$

F$($t$)=2$sin$(3$t$)$N

What is the particular solution component to the position at t$=3$sec in x$.\backslash$times x

format?

Question $8$

For a mass$-$spring$-$damper system the governing equation is:

x$^()+16$x$=$sin$(4$t$)$

Determine the position, using x$.\backslash$times x format, at t$=8$sec if the system starts

from x$(0)=$x$\_($o$)=0\mathrm{.}3$m with an initial velocity of $-0\mathrm{.}5($m$)/($s$)$