Example 1 - Waveform Representation

Example:

a) What is the period of this waveform?
b) Find equations representing the waveform over the first period
(ie 0 ≤ t ≤ 10).
c) Find equations representing the waveform over the second period
(ie 10 ≤ t ≤ 20).

Solution:
a) The period is the time of  one full cycle
T = 10 seconds

b) Equation for line (1) 0 ≤ t ≤ 4; (v in volts, t in seconds)
v(t) = m t + b; m = ∆v / ∆t = (v2 - v1) / (t2 - t1) = (8-0) / (4-0) = 2
\ v = 2 t + b; b = 0, by inspection of graph
\ v = 2 t;  (0 ≤ t ≤ 4)

Equation for line (2) 4 ≤ t ≤ 10; (v in volts, t in seconds)
v(t) = m t + b; m = ∆v / ∆t = (v2 - v1) / (t2 - t1) = (0-8) / (10-4) = -8 / 6 = -4 / 3 » -1.33
\ v = - 4/3 t + b; to find "b", note that line (2) passes thru point (10, 0)
\ 0 = -4/3 (10) + b; --> b = 40/3
\ v = - 4/3 t + 40/3; (4 ≤ t ≤ 10)
or OK to write
v = -1.33 t + 13.33; (4 ≤ t ≤ 10)

b) Find equations for line segments representing second period (10 ≤ t ≤ 20)
easy if we shifting concept
v = 2(t - T)
v = 2(t - 10) or v = 2t - 20; (10 ≤ t ≤ 14)v = -4/3(t - 10) + 40/3 or v = -4/3t + 80/3; (14 ≤ t ≤ 20)

Note: could proceed in similar fashion to find equations for other cycles or periods.