Teaching JKPSC Lecturership Mock Test Series 2024-25 Physical Sciences Mathematical Methods of Physics Fourier Transforms and Laplace Transforms
The Fourier series of complex waveforms of earthquakes is simplified and written as \(f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \alpha_n \cos(nx - \theta_n). \) The value of \(a_n^2 + b_n^2\) is
1
\(\alpha_n^2(1+\sin 2\theta_n) = a_n^2 + b_n^2\)
2
\(\alpha_n^2(1+2\sin \theta_n) = a_n^2 + b_n^2\)
3
\(\alpha_n^2 = a_n^2 + b_n^2\)
4
\(\alpha_n^2(1+\sin \theta_n) = a_n^2 + b_n^2\)