A testing device consists of a pneumatic cylinder that accel

A testing device consists of a pneumatic cylinder that accelerates a piston and 5 kg assembly to a speed of 30 m/s. At that instant, the assembly is decelerated by engaging a spring and dashpot. The spring has a stiffness of 50 N/mm and the dashpot is damped with a constant of 1000 N·s/m. Do the following: (a) Determine whether the system is underdamped, overdamped, or critically damped. You must show calculations to support your answer. (b) Taking the initial displacement to be zero, determine the time at which the maximum displacement of the piston occurs after the spring and dashpot are engaged. You must show all calculus and algebraic steps in order to receive full credit. (c) Using the answer to part (b), determine the maximum displacement of the piston.

Solution

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