Your boss would like to know the gain and phase of the above sensor for an excitation frequency of 4 radians per second. Knowing that multiplying a signal in the Laplace domain by the Laplace variable, s, is analogous to differentiating the signal, you realize that the sensor’s dynamics in the above problem are equivalent to thefollowing differential equation: dy/dt + y(t) = 0.1u(t)1
Begin by assuming that y(t) = Asin(4t), for some unknown constant, A. Solve for dy/dt and use dt' the above differential equation to solve for u(t).
2. Sketch a phasor diagram that allows you to determine the magnitude and phase of u(t) relative to y(t).
3. Determine the gain of this sensor at the above excitation frequency, in Volts per Celsius, defined as the magnitude of y(t) divided by the magnitude of u(t).
4. Determine the phase of this sensor at the above excitation frequency, in either radians or degrees (please indicate which), defined as the phase of y(t) relative to u(t).