Calculating the period of a harmonic function

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To calculate the period of the harmonic function x=16cos(10t+5π/3), the relevant formula is T=2π/a, where 'a' is the coefficient of 't' in the cosine function. In this case, 'a' is 10, so the period is T=2π/10. The phase constant (5π/3) does not affect the period or frequency of the function. For a more complex function like x(t)=4sin(15t)-3cos(9t+1.1), the periods of the individual components must be determined separately, which can be challenging analytically. The discussion highlights the importance of understanding how phase shifts influence harmonic functions.
No0bzDown
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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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You cos function repeats when 10t increased by 2 \pi. See if you can work it out based on that.
 
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 ?
 
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.
 
Nice. Thanks very much.
 
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...
 
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