I came up with this function by using Fourier transform. My only problem is how to get the amplitude of this function. Im planning to get the difference between their maxima and minima. I get its first derivative then equate it to zero then plug the value of $x$ to the original function but the value of $x$ is just one. I need to get two critical points at least. But I just got one.
This is the function:
$ f(t) = 9.364984 -\frac{5441 \cos(2π(8.141334)(t-2456349.714))}{200000}+\frac{1481 \cos(2π(16.282667)(t-2456349.714))}{250000} +\frac{17397 \sin(2π(8.141334)(t-2456349.714))}{125000} - \frac{10557 \sin(2π(16.282667)(t-2456349.714))}{500000} -\frac{1139 \cos(2π(24.424001)(t-2456349.714))}{200000}+\frac{29 \cos(2π(32.565334)(t-2456349.714))}{50000} + \frac{753 \sin(2π(24.424001)(t-2456349.714))}{250000} - \frac{\sin(2π(32.565334)(t-2456349.714))}{200000} $
Let $\theta = 2\pi\times8.141334\times(t-2456349.714)$ ignore the constant term 9.364984, the function to optimize then becomes
$$ g(\theta) = \frac{5441}{200000}\cos\theta + \frac{1481}{250000}\cos 2\theta + \frac{17397}{125000}\sin\theta - \frac{10557}{500000}\sin2\theta - \frac{1139}{200000}\cos 3\theta + \frac{29}{50000}\cos4\theta + \frac{753}{250000}\sin3\theta-\frac{1}{200000}\sin4\theta $$
Thus the derivative is also some linear combination of sine and cosine of $\theta, 2\theta, 3\theta, 4\theta$. Using $\sin^2x+\cos^2x=1\implies\sin\theta=\pm\sqrt{1-\cos^2\theta}$ and the multiple angle formulas the trigonometric equation $g'(\theta)=0$ can then be reduced to an octic (degree-8) equation of $\cos\theta$, which for sure does not have any general closed form exact solution.
Therefore, the maximum and minimum can only be solved numerically. (The maximum is attained at $\theta = 2.038368167$ and minimum at $\theta = 4.507982189$, by the way.)
Note that the root mean square $\sqrt{\frac1T \int_0^T f(t)^2dt}$ can be computed quite easily instead of the amplitude.