A micromechanical resonator is vibrating at the frequency fo = 20 kHz with vibration aplitude x0 = 10 nm. The vibrations are measured using the rate-of-change measuremnent with a parallel plate capacitor that has the area A - 1000 um^2 and the gap d = 1um. Calculate the motional current if the bias voltage over the capacitor is Vdc = 5 V.

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.