Find the steady-state expression for vo(t) if vg=60sin50,000tv. suppose that vo(t)=v0cos(ωt+ϕ), where −180∘< ϕ≤180∘. determine the values v0,ω, and ϕ. express your answers using three significant figures separated by commas. express v0 in volts, ω in radians per second, ϕ in degrees.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.