Reference no: EM13910612

1. A certain electric current is pulsating so that the current as a function of time is given by

Find the constant term, a₀, the first four cosine terms, and the first four sine terms of the Fourier series for this pulsating current. Calculate the Fourier series integrals by hand (i.e., no calculator or computer computation of the Fourier series for this problem). Use the integral table as needed. Use Desmos to graph three periods of the function f(t) and the Fourier series you found. Print out your graph to turn in.

2. According to Newton's Law of Cooling, the rate at which a body cools is proportional to the difference in temperature between it and the surrounding medium. An object whose temperature is 100 °C is placed in a medium whose temperature is 20 °C. The temperature of the object falls to 50 °C in 10 minutes. Assuming Newton's Law of Cooling applies, express the temperature, T, of the object as a function of time t (in minutes).