Calculating the period of a harmonic function

In summary, the period of a harmonic function with both cos and sin terms can be calculated analytically. For example, if we have the function x(t)=4sin(15t)-3cos(9t+1.1), the period can be found using the formula T=2π/a, where a is the coefficient of the variable inside the trigonometric function. In this case, the period would be 2π/15 for the sin term and 2π/9 for the cos term. To find the overall period, we can take the least common multiple of these two values, which is 2.1. This matches the period of 2.1 found by plotting the function in MATLAB. Therefore
  • #1
No0bzDown
3
0
For a example, x=16cos(10t+5π/3) ,S.I.

How am i supposed to calculate the period?(in order to do the graph)


Thanks in advance
 
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  • #2
You cos function repeats when 10t increased by [itex]2 \pi[/itex]. See if you can work it out based on that.
 
  • #3
If we have something like this: f(x) = cos(at)

then T= 2π/a

But i really want to know if on my first example 5π/3 is playing any role on this formula.

I mean if x=16cos(10t + 5π/3)

Is period still T = 2π/a = 2π/10 ?
 
  • #4
No0bzDown said:
If we have something like this: f(x) = cos(at)

then T= 2π/a

But i really want to know if on my first example 5π/3 is playing any role on this formula.

I mean if x=16cos(10t + 5π/3)

Is period still T = 2π/a = 2π/10 ?

Yes it is. The phase constant (5 Pi /3) does not change the frequency or period.
 
  • #5
Nice. Thanks very much.
 
  • #6
What if you have a harmonic function with both cos and sin?

such as: x(t)=4sin(15t)-3cos(9t+1.1)

can you find the period of this analytically? I have found this has a period of 2.1 by plotting it in MATLAB, but can't figure out how to calculate this analytically...
 
Last edited:

What is a harmonic function?

A harmonic function is a mathematical function that satisfies the Laplace equation, which is a partial differential equation that describes the relationship between the values of a function at different points in space.

What is the period of a harmonic function?

The period of a harmonic function is the length of time it takes for the function to repeat itself. It is the smallest positive value of t for which the function f(t) = f(t + T) for all values of t. In simpler terms, it is the length of one complete cycle of the function.

How do you calculate the period of a harmonic function?

The period of a harmonic function can be calculated using the formula T = 2π/ω, where T is the period and ω is the angular frequency of the function. ω is equal to 2π times the frequency of the function, which is the number of cycles per unit time.

What is the difference between angular frequency and frequency?

Angular frequency and frequency are related, but they are not the same thing. Frequency refers to the number of cycles per unit time, while angular frequency is the rate of change of an angle per unit time. Angular frequency is equal to 2π times the frequency of the function.

What is the significance of calculating the period of a harmonic function?

Calculating the period of a harmonic function is important in understanding the behavior and patterns of the function. It allows us to predict when the function will repeat itself and how it will change over time. This can have practical applications in fields such as physics, engineering, and economics.

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