Consider the following equation: $$Eq. 1\qquad f(t) = a(t) \sin(\omega t) + r(t)$$ where function $f(t)$ is known and functions $a(t)$ and $r(t)$ are unknowns. It is aimed to find these two unknown functions. Differentiating both side of above equation would result in following: $$Eq. 2\qquad f'(t) = a'(t)\sin(\omega t) + wa(t)\cos(\omega t) + r'(t)$$ Is it possible to consider $Eq. 2$ as an independent equation and consider both equations as a system to solve for unknown functions, either analytically or numerically?
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What have you tried? See How to ask a good question. – Ѕᴀᴀᴅ Apr 30 '20 at 08:23
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1To solve what for what ? What is known and what is unknown ? – JJacquelin Apr 30 '20 at 08:43
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As I stated the f(t) is known and a(t) and r(t) are unknowns. – Pirooz Apr 30 '20 at 09:20
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What do you want to solve, Have you other conditions on $a$ and $r$ like periodicity ? – EDX Apr 30 '20 at 09:49
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Function a(t) is always positive. Function r(t) possesses negative, zero and positive values same as function f(t). These are all we know. – Pirooz Apr 30 '20 at 12:07