Two waveforms, υ1(t) and υ2(t), have identical amplitudes and oscillate at the same frequency, but υ2(t) lags υ1(t) by a phase angle of 60°. If υ1(t) = 4 cos(2π × 103t + 30° ) V,

Required:
Write the expression appropriate for υ2(t) and plot both waveforms over the time span from −1 ms to +1 ms.

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

Coiled springs ought to be very strong and stiff. si3n4 is a strong, stiff material. would you select this material for a spring? explain.