Sinusoidal Functions: Max/Min Volts in 1s w/ t-Values

In summary: The n = 1 zero is at 5t = \frac{3\pi }{2} , so t = \frac{3\pi }{10} .In summary, The voltage of a power supply, V(t), can be represented by the function V(t) = 110sin5t+15, where t is the time in seconds. In order to find the maximum and minimum voltages within the first second, we can use the derivative of the function, v'(t)=550cos5t, and solve for 5t = \frac{\pi }{2} + n\pi, where n is an integer. This
  • #1
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Homework Statement



The voltage, V(t), in volts, of a power supply can be modeled by the function V(t) = 110sin5t+15, where t is the time, in seconds. Find the maximum and minimum voltages, within the first second, and the times they occur.


Homework Equations





The Attempt at a Solution



well, i think since the period is 5? that means there are 5 cycles, which means there will be 5 maximums, and 5 minimums, how do i figure out where the exact points are maximum?

v'(t)=550cos5t

but how do i solve t there?
 
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  • #2
You are correct to think that there will be 5 cycles. However, that is 5 cycles per 2[tex] \pi[/tex] radians. In order to find the zeros for your derivative, think about when does Cos(5t) = 0? It is equal to 0 whenever the argument inside cosine is [tex]\frac{\pi }{2} + n\pi [/tex]. Thus you can solve for [tex] 5t = \frac{\pi }{2} + n\pi \\ [/tex] with n = 0, 1, 2, 3... but remember, only with t<1 second.
 
  • #3
What do you mean with "n"?
 
  • #4
Draggu said:
What do you mean with "n"?

n is an integer of 0,1,2,3... etc etc. Remember, cosines and sines go on forever and they have an infinite number of zeros. The n tells you which zero you are at. For example, the n = 0 zero is at 5t = [tex]\frac{\pi }{2} [/tex]
 

1. What are sinusoidal functions?

Sinusoidal functions are mathematical functions that represent a repeating pattern of values over time. They are often used to model real-world phenomena such as sound waves, electromagnetic waves, and the behavior of oscillating systems.

2. How do you calculate the maximum and minimum volts in a sinusoidal function?

The maximum and minimum volts in a sinusoidal function can be calculated using the amplitude and the vertical shift of the function. The amplitude is the distance from the midline to the maximum or minimum value, and the vertical shift is the amount the graph is shifted up or down from the x-axis. The maximum voltage can be calculated by adding the amplitude to the vertical shift, and the minimum voltage can be calculated by subtracting the amplitude from the vertical shift.

3. What is the significance of 1s in sinusoidal functions?

1s in sinusoidal functions represents one full cycle of the repeating pattern. This means that the function will repeat itself every 1 second, and the maximum and minimum values will occur once within that time period.

4. What do t-values represent in sinusoidal functions?

t-values represent time in sinusoidal functions. They are used to track the changes in the function over time and to determine the frequency of the repeating pattern. The t-values are usually measured in seconds.

5. How are sinusoidal functions used in practical applications?

Sinusoidal functions are used in various practical applications, such as in electrical engineering, physics, and signal processing. They can be used to analyze and predict the behavior of oscillating systems, model sound and electromagnetic waves, and design electronic circuits and devices that rely on sinusoidal signals.

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