MODERATE EXERCISES-Modelling with Trigonometric Functions

(1) he voltage, V, of an electrical outlet in a home is given as a function of time, t (in seconds), by

V = V_o cos(120 t).

1. What is the period of the oscillation?
2. What does V_o represent?
3. Sketch the graph of V against t. (Take V_o to be some unknown positive quantity.) Label the axes.
4. If V_o is 0.5 volts, what is the voltage at time t = 30?
5. If V_o is 0.5 volts, what is the first time when the voltage is 0.25 volts?

SOLUTION:

(a) 1/60 seconds

(b) Vo represents the maximum voltage, or the amplitude of fluctuation

(c) 

(d) When Vo = 0.5 V and t = 30 s, V(30) = 0.5 V

(e) If Vo = 0.5 V, the first time V(t) = 0.25 V is at t = 1/360 s