UPSC ESE 2025 Mechanical Engineering Paper

(a)Statement 1: Mechanical impedance at an interaction port can be defined as a dynamic operator that determines an output force in response to an input velocity at the same port.Statement 1 is Correct.Mechanical impedance is defined as the ratio of force to velocity, typically in the frequency or Laplace domain. It characterizes how a system resists motion under force - a core idea in impedance control.Statement 2: A mechanical admittance is a dynamic operator that determines an output velocity in response to an input force.Statement 1 is Correct. Admittance is the inverse of impedance. It defines how a system responds with velocity to an applied force- useful in admittance control schemes.Statement 3: For linear systems, admittance is proportional to impedance, and both can be represented as transfer functions in Laplace domain.Statement 3 is Incorrect. In linear systems, admittance is the inverse of impedance, not proportional.- If $Z(s)$ is impedance, then $Y(s)=\frac{1}{Z(s)Y(s)}$ is admittance. So, this statement is mathematically inaccurate.