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Oscillations

# The mean position and one extreme position of the two different waves represented by $x=10-20 \sin(8t)$ and $x=12+21sin(3t)$ respectively are:

$\begin{array}{1 1}(a)\;46,0,28,-22 \\(b)\;10,-10,12,-9 \\( c)\; 23,0,28,46 \\(d)\; 0,23,5,-18 \end{array}$

Motion of sea waves through it may look random it is actually a combination of number of SHMs of different frequency & amplitude.
These waves have been studied characterized by their power spectnal density (PSD) as a function of frequency.
The PSD is nothing but square of max acceleration divided by a small frequency sample in which acceleration is assumed to be constant.
This is a meat means of representing such seemingly random phenomenon.
This technique is used to describe wind velocities which are gusty, the vibrations experienced in a motor car, aeroplane, etc.
Hence b is the correct answer