Assume that the Heaviside function defined by
H(t) = {0ift<01ift≥0
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≤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 = 120−060−0=2
c.) Find a formula for V(t) in terms of H(t) for t≤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 = 100−032−7=4
Tuesday, March 15, 2016
Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 58
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