The Heaviside function defined in Exercise 59 can also be used to define the ramp function y = ctH ( t ) , which represents a gradual increase in voltage or current in a circuit. (a) Sketch the graph of the ramp function y = tH ( t ) . (b) 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. Write a formula for V ( t ) in terms of H ( t ) for t ≤ 60. (c) 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. Write a formula for V ( t ) in terms of H ( t ) for t ≤ 32.
The Heaviside function defined in Exercise 59 can also be used to define the ramp function y = ctH ( t ) , which represents a gradual increase in voltage or current in a circuit. (a) Sketch the graph of the ramp function y = tH ( t ) . (b) 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. Write a formula for V ( t ) in terms of H ( t ) for t ≤ 60. (c) 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. Write a formula for V ( t ) in terms of H ( t ) for t ≤ 32.
The Heaviside function defined in Exercise 59 can also be used to define the ramp functiony = ctH(t), which represents a gradual increase in voltage or current in a circuit.
(a) Sketch the graph of the ramp function y = tH(t).
(b) 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. Write a formula for V(t) in terms of H(t) for t ≤ 60.
(c) 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. Write a formula for V(t) in terms of H(t) for t ≤ 32.
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