What is the fundamental period of the function f(t)= sin6t + cos8t?

In summary, the fundamental period of f(t) = sin6t + cos8t is the smallest value of T such that f(t+T) = f(t). The fundamental period of the first term is pi/3 and the second term is pi/4. To find the fundamental period of the entire function, we cannot simply add the two periods together. We can use trigonometric sum of angle formulas to solve the equation explicitly, or we can find common multiples. It would be unethical to give the answer away without attempting to solve the problem ourselves.
  • #1
Luongo
120
0
1. what's the fund. period of f(t)= sin6t + cos8t?
2. the fund period of the first term is pi/3, the second pi/4
3. do i just add the 2 fundamental periods up to get the whole fund period? also for the Fourier coefficients of this function, should i use euler's to make it into exponentials before i integrate to avoid by parts method? or just integrate as is.
 
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  • #2
What is the definition of the fundamental period? Does the sum of pi/3 and pi/4 satisfy the definition?
 
  • #3
fzero said:
What is the definition of the fundamental period? Does the sum of pi/3 and pi/4 satisfy the definition?
you're just asking me what I'm asking you in other words
im not sure. the fund freq is the smallest period for the function and pi/3 and pi/4 are those... summed right
 
  • #4
I'm asking you because you don't seem to understand the definition and that's where we need to start to do this problem. The (fundamental) period of a function is the smallest value of T such that f(t+T) = f(t). You should verify that your guess doesn't satisfy this.

It's unnecessary to try to guess at solutions. You can use the trig sum of angle formulas to solve this equation explicitly. Otherwise you have to know something about common multiples.
 
  • #5
fzero said:
I'm asking you because you don't seem to understand the definition and that's where we need to start to do this problem. The (fundamental) period of a function is the smallest value of T such that f(t+T) = f(t). You should verify that your guess doesn't satisfy this.

It's unnecessary to try to guess at solutions. You can use the trig sum of angle formulas to solve this equation explicitly. Otherwise you have to know something about common multiples.


can you save me the misery and tell me what it is? i work better once i have the solution is it pi?
 
  • #6
Luongo said:
can you save me the misery and tell me what it is? i work better once i have the solution is it pi?

It would be unethical (and against the forum rules) to give the answer away when you won't attempt to work on the problem for yourself.
 
  • #7
the smallest period for both is PI. thus PI should be the fund period of the sum of the two is this logic right/
 
  • #8
I have the same question and I know the fundamental period is the smallest period of a function. So if we break apart the function f(x) we know that sin(6t) has a fundamental period of pi/3 and for cos(8t) the fundamental period is pi/4. I'm not quite sure how we can add these and i tried simplifying using identies but didn't get anywhere. What should be my next step?
 

What is the fundamental period?

The fundamental period, also known as the fundamental frequency, is the lowest frequency at which a system or object can vibrate and still maintain its shape and form. This frequency is unique to each system and is determined by its physical properties.

How is the fundamental period calculated?

The fundamental period can be calculated using the formula T = 1/f, where T is the period (in seconds) and f is the frequency (in Hertz). In other words, the fundamental period is equal to the inverse of the fundamental frequency.

Why is the fundamental period important?

The fundamental period is important because it can provide valuable information about a system or object. For example, the fundamental period of a structure can help engineers determine its natural frequency, which is crucial for earthquake-resistant design.

How does the fundamental period relate to harmonics?

The fundamental period is the first harmonic, or the lowest frequency, of a system. Higher harmonics are integer multiples of the fundamental frequency. This means that a system with a fundamental period of 2 seconds will also have harmonics at 4 seconds, 6 seconds, and so on.

Can the fundamental period change?

Yes, the fundamental period can change depending on the properties of the system or object. For example, the fundamental period of a guitar string can change by adjusting its tension or length. The fundamental period can also change when a system is affected by external forces, such as wind or vibrations.

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