Question $1$

mx$^()+$kx$=0$

m$=6$kg

k$=68($N$)/($m$)$

What is the position at t$=2$sec $?$

The system starts at rest at an initial position of x$(0)=0\mathrm{.}5$m

Question $2$

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

mx$^()+$cx$^()+$kx$=0$

m$=6$kg

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

k$=73($N$)/($m$)$

Determine the position, using x$.\backslash$times x format, at t$=5$sec if the system starts

from x$(0)=$x$\_($o$)=0\mathrm{.}1$m with an initial velocity of $0($m$)/($s$)$

Question $3$

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

mx$^()+$cx$^()+$kx$=0$

m$=5$kg

k$=94($N$)/($m$)$

Determine the damping coefficient, c $,$ in xx $.$x format such that the system is

critically damped.

Question $4$

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

mx$^()+$cx$^()+$kx$=0$

m$=5$kg

k$=33($N$)/($m$)$

The system is critically damped. If the initial position is $0\mathrm{.}4$ m and the initial

velocity is $0($m$)/($s$),$ what is the position at t$=1\mathrm{.}9$sec using x$.\backslash$times x format?

Question $5$

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

mx$^()+$cx$^()+$kx$=0$

m$=6$kg

c$=94$N$^(*)($s$)/($m$)$

k$=86($N$)/($m$)$

Determine the position, using x$.\backslash$times x format, at t$=6$sec if the system starts

from x$(0)=$x$\_($o$)=0\mathrm{.}6$m with an initial velocity of $0\mathrm{.}1($m$)/($s$)$