The heaviside function h is defined by h(t)={0 if t< 0, 1 if t≥0 it is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on. sketch the graph of the voltage v(t) in a circuit if the switch is turned on at time t=5 seconds and 240 volts are applied instantaneously to the circuit. write a formula for v(t) in terms of h(t). (note that starting at t=5 corresponds to a translation.)

Explanation:

The heaviside function is defined as:

so we see that the Heaviside function "switches on" when, and remains switched on when

If we want our heaviside function to switch on when , we need the argument to the heaviside function to be 0 when

Thus we define a function f:

The term inside the heaviside function makes sure to displace the function 5 units to the right.

Now we just need to add a scale up factor of 240 V, because thats the voltage applied after the heaviside function switches on. ( when , so it becomes just a 1, which we can safely ignore.)

Therefore our final result is:

I have made a sketch for you, and added it as attachment.  

u=13

v=30

s/t=u+1\2at

=13+431/2

=13+265.5

=278.5

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