A spring-mass-damper system is fixed to its base. Assuming that x(t) denotes the position of the mass with respect to time, determine the equation of motion of the Rev A: Prof. Bryan W. Weber Page 2 of 5 Spring 2020 system. Sketch plots of the step response of the system when it is (a) underdamped, (b) critically damped, (c) overdamped.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.