Assume that the Heaviside function defined by
$H(t)$ = $\left\{\begin{array}{cccc}
0 & if & t < 0 \\
1 & if & t\geq 0
\end{array} \right.$
can also be used to define the ramp function $y= tH(t)$, which represents a gradual increase in voltage or current in a circuit.
a.) Draw the graph of the ramp function $y = tH(t)$.
b.) Find a formula for $V(t)$ in terms of $H(t)$ for $t \leq 60$ and sketch the graph of the voltage V(t) in a circuit if the switch is turned on at time t = 0 and the voltage is gradually increased to 120 volts over a 60-second time interval.
slope = $\frac{120 - 0}{60 - 0} = 2$
c.) Find a formula for $V(t)$ in terms of $H(t)$ for $t \leq 32$ and sketch the graph of the voltage $V(t)$ in a circuit if the switch is turned on at time $t = 7$ seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds.
slope = $\frac{100 -0}{32-7} = 4$
Tuesday, March 15, 2016
Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 58
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