Answer Happy

1 Mass-Spring-Damper System: Step Response The equation for a mass-spring-damper system with a step signal input may be written as Mÿ(t) + Dÿ(t) + Ky(t) = v(t). (1) Here y is the output, which is the displacement of the mass, v is the input force. The “damper" in the name of the system refers to friction, which is proportional to velocity. The greater the parameter D the greater the viscosity of the medium in which the mass-spring system is placed. For further questions, assume that M = 0.5, D = K = 1 and that v = u is the step signal. 1. PRE-WORKSHOP: To find the step response, we assume the system is initially at rest: y(0) = y(0) = 0. Use Laplace transforms in (1) to obtain an expression for Y(s).