In a diode circuit, where an AC voltage vIN, with a DC offset of 5 V and AC amplitude of 10 mV, is applied to a 1 MΩ resistor and a PN junction diode. Let’s express vIN = VIN + vin, where VIN = 5 V is the DC offset and vin = 10 cos(t + ϕ) mV is the AC component. Since vIN oscillates between 4.99 V (= 5 − 0.01) and 5.01 V (= 5 + 0.01), the diode is always in reverse bias. Required:
Draw the Vout waveform when the diode has 0.7V voltage drop.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Aflywheel accelerates for 5 seconds at 2 rad/s2 from a speed of 20 rpm. determine the total number of revolutions of the flywheel during the period of its acceleration. a.5.65 b.8.43 c. 723 d.6.86

Hydraulic fluid with a sg. of 0.78 is flowing through a 1.5 in. i.d. pipe at 58 gal/min. the fluid has an absolute viscosity of 11.8 x 105 lbf-sec/ft2. is the flow laminar, turbulent or within the critical range? give both a numerical reynolds number and a term answer.