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Solution => Given:FBD:Equation of mation for mars m_(1) Balance all the forces in horizontal direction{:[=>m_(1)x^(¨)_(1)+b_(1)x^(˙)_(1)+k_(1)x_(1)-k_(3)(x_(2)-x_(1))=4],[=>m_(1)x^(¨)_(1)+b_(1)x^(˙)_(1)+(k_(1)+k_(2))x_(1)-k_(3)x_(2)=4_(2)]:}Equation of motion for mass m_(2) Balance all the forces in horizontal direstion{:[=>m_(2)x^(¨)_(2)+b_(2)x^(˙)_(2)+k_(2)x_(2)+k_(3)(x_(2)-x_(1))=0],[=>m_(2)x^(¨)_(2)+b_(2)x^(˙)_(2)+(k_(2)+k_(3))x_(2)-k_(3)x_(1)=0]:}Nom, take Laplace equation (1) &(2){:[=>m_(1)L{x^(¨)_(1)}+b_(1)L{r^(˙)_(1)}+(k_(1)+k_(2))L{x_(1)}-k_(3)L{k_(2)}=L{4}],[&],[=>m_(2)L{x^(¨)_(2)}+b_(2)L{x^(˙)_(2)}+(k_(2)+k_(3))L{x_(2)}-k_(3)L{x_(1)}=0]:}from eqns (3) 4 (4){:[m_(1)s^(2)x_(1)(s)+b_(1)sx_(1)(s)+(k_(1)+k_(3))x_(1)(s)],[-k_(3)x_(2)(s)=U(s)],[(m_(1)s^(2)+b_(1)s+(k_(1)+k_(3))x_(1)(s)=k_(3)x ... See the full answer

Solution => Given:FBD:Equation of mation for mars m_(1) Balance all the forces in horizontal direction{:[=>m_(1)x^(¨)_(1)+b_(1)x^(˙)_(1)+k_(1)x_(1)-k_(3)(x_(2)-x_(1))=4],[=>m_(1)x^(¨)_(1)+b_(1)x^(˙)_(1)+(k_(1)+k_(2))x_(1)-k_(3)x_(2)=4_(2)]:}Equation of motion for mass m_(2) Balance all the forces in horizontal direstion{:[=>m_(2)x^(¨)_(2)+b_(2)x^(˙)_(2)+k_(2)x_(2)+k_(3)(x_(2)-x_(1))=0],[=>m_(2)x^(¨)_(2)+b_(2)x^(˙)_(2)+(k_(2)+k_(3))x_(2)-k_(3)x_(1)=0]:}Nom, take Laplace equation (1) &(2){:[=>m_(1)L{x^(¨)_(1)}+b_(1)L{r^(˙)_(1)}+(k_(1)+k_(2))L{x_(1)}-k_(3)L{k_(2)}=L{4}],[&],[=>m_(2)L{x^(¨)_(2)}+b_(2)L{x^(˙)_(2)}+(k_(2)+k_(3))L{x_(2)}-k_(3)L{x_(1)}=0]:}from eqns (3) 4 (4){:[m_(1)s^(2)x_(1)(s)+b_(1)sx_(1)(s)+(k_(1)+k_(3))x_(1)(s)],[-k_(3)x_(2)(s)=U(s)],[(m_(1)s^(2)+b_(1)s+(k_(1)+k_(3))x_(1)(s)=k_(3)x ... See the full answer