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The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given by
a) (-1)^n
b) sin(npi/2)/n pi
c)I sin npi /2
d)n pi?
a) (-1)^n
b) sin(npi/2)/n pi
c)I sin npi /2
d)n pi?
Most Upvoted Answer
The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dira...
Explanation:
Fourier Coefficients Calculation:
- The Fourier coefficients an can be calculated using the formula: an = (1/T) ∫f(t)e^(-2πint/T) dt
- Given that the spikes are located at t=1/2(2n-1), which are Dirac delta functions of strength ±1, the Fourier coefficients can be determined.
Calculation of Fourier Coefficients:
- Since the spikes occur at t=1/2(2n-1), the Fourier coefficients can be calculated by taking the integral of f(t) multiplied by e^(-2πint/T) over one period.
- For n=0, the coefficient is 0 since there are no spikes at t=0.
- For n=±1, the coefficient will be ±1/T, depending on the sign of the spike.
- For n=±2, the coefficient will be 0 again since there are no spikes at t=T/2 or -T/2.
Final Answer:
- Therefore, the Fourier coefficients an will be of the form (-1)^n, which corresponds to option a) in the given choices.
Fourier Coefficients Calculation:
- The Fourier coefficients an can be calculated using the formula: an = (1/T) ∫f(t)e^(-2πint/T) dt
- Given that the spikes are located at t=1/2(2n-1), which are Dirac delta functions of strength ±1, the Fourier coefficients can be determined.
Calculation of Fourier Coefficients:
- Since the spikes occur at t=1/2(2n-1), the Fourier coefficients can be calculated by taking the integral of f(t) multiplied by e^(-2πint/T) over one period.
- For n=0, the coefficient is 0 since there are no spikes at t=0.
- For n=±1, the coefficient will be ±1/T, depending on the sign of the spike.
- For n=±2, the coefficient will be 0 again since there are no spikes at t=T/2 or -T/2.
Final Answer:
- Therefore, the Fourier coefficients an will be of the form (-1)^n, which corresponds to option a) in the given choices.
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The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi?
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The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi?.
The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The spikes are located t=1/2(2n-1), at where n=0,+-1,+-2,,,,, are dirac delta function of strength+-1. the amplitude an in the Fourier expansion f(t)= submission - ♾️ to +♾️ ane^(2pi int/T) are given bya) (-1)^nb) sin(npi/2)/n pic)I sin npi /2d)n pi?.
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