railway RRB JE (CBT I + CBT II) Mock Test 2024 Control Systems Basics of Control Systems Type and Order of System
Consider a mechanical system shown in the figure. Masses are free to slide over a frictionless horizontal surface. The equation of motion of mass m1 is:
1
\({{m}_{1}}{{\overset{\ddot{\ }}{\mathop{x}}\,}_{1}}+\left( {{\lambda }_{1}}+{{\lambda }_{2}} \right){{\dot{x}}_{1}}+{{\lambda }_{2}}{{\dot{x}}_{2}}-\left( {{k}_{1}}+{{k}_{2}} \right){{\dot{x}}_{1}}-{{k}_{2}}{{x}_{2}}={{F}_{2}}\)
2
\({{m}_{2}}{{\overset{\ddot{\ }}{\mathop{x}}\,}_{1}}+\left( {{\lambda }_{1}}-{{\lambda }_{2}} \right){{\dot{x}}_{1}}+{{\lambda }_{2}}{{\dot{x}}_{2}}-\left( {{k}_{1}}+{{k}_{2}} \right){{\dot{x}}_{1}}-{{k}_{2}}{{x}_{2}}={{F}_{1}}\)
3
\({{m}_{1}}{{\overset{\ddot{\ }}{\mathop{x}}\,}_{1}}+\left( {{\lambda }_{1}}+{{\lambda }_{2}} \right){{\dot{x}}_{1}}-{{\lambda }_{2}}{{\dot{x}}_{2}}+\left( {{k}_{1}}+{{k}_{2}} \right){{\dot{x}}_{1}}-{{k}_{2}}{{x}_{2}}={{F}_{1}}\)
4
\({{m}_{1}}{{\overset{\ddot{\ }}{\mathop{x}}\,}_{1}}+\left( {{\lambda }_{1}}-{{\lambda }_{2}} \right){{\dot{x}}_{1}}+{{\lambda }_{2}}{{\dot{x}}_{2}}-\left( {{k}_{1}}-{{k}_{2}} \right){{\dot{x}}_{1}}-{{k}_{2}}{{x}_{2}}={{F}_{2}}\)