The sawtooth waveforms are used to control the horizontal and vertical motion of an
electron beam that sweeps across the screen. The vertical deflection sawtooth waveform
is responsible for moving the electron beam from the top of the screen to the bottom (this
is known as trace) and back again (retrace). To prevent flickering, the time needed to
perform this “painting” must be completed within 1/60 seconds.
One method of generating such a waveform is to repeatedly charge a capacitor with a
large time constant, and repeatedly discharges it with a very small time constant. The
sawtooth generation circuit and its waveform is shown in Figure 2

http://imageshack.us/photo/my-images/507/pbilsh4.png/

Question:

With reference to the sawtooth waveform in Figure 2, calculate the value of R1 in order to produce the charging voltage shown. Use Laplace Transform to find the answer.

Hint:
Use V = iR1 Vc(t) to find I(t).
Then use V(c)= V-iR1 to find R1.