Derive the equation for the displacement response of a viscously damped SDF system due to ini- tial velocity u(0) for three cases: (a) underdamped systems; (b) critically damped systems; and (c) overdamped systems. Plot u(t) ÷ ü(0)/w, against t/T, for =0.1, 1, and 2.

A h HU y h An object of mass 0.3 kg is released by pushing down a little (y) while floating with h-20 cm submerged in water. a) Write the differential equation of the free oscillations of the system, assuming that, during the motion, the body is subjected to a damping force given by -bv (v is the velocity of the body. b is the damping constant). b) If the frequency of the damped harmonic motion is half the frequency when there is no damping, what is the value of the damping constant?

! Required information Sometimes manometer dimensions have a significant effect. In the given image, the containers (a) and (b) are cylindrical and conditions are such that Pa = Pb, for d= 0.2D. L D (a) Water Numeric Response -d D (b) SAE 30 oil H Take y=9790 N/m³ for water and 8720 N/m³ for SAE 30 oil. Comparing the above two cases, what is the percentage change in the value of Ap?

Sketch the level response for a bathtub with cross-sectional area of 8 ft 2 as a function of time for the following sequence of events; assume an initial level of 0.5 ft with the drain open. The inflow and outflow are initially equal to2ft3/min.(a)The drain is suddenly closed, and the inflow remains con-stant for 3 min (0≤t≤3).(b)The drain is opened for 15 min; assume a time constant in a linear transfer function of 3 min, so a steady state is essentially reached (3≤t≤18) (c)The inflow rate is doubled for 6 min (18≤t≤24).(d)The inflow rate is returned to its original value for 16 min(24≤t≤40).