For option (A) \( \phi = kt + C \) it can be 1D motion eg -> \( x = A \sin \phi \)
(SHM) For option (B) \( v^2 + x^2 = \) constant yes 1D
For option (C) time can't be negative Not possible
For option (D) Possible A, B and D only
Let $ f: \mathbb{R} \to \mathbb{R} $ be a twice differentiable function such that $$ f''(x)\sin\left(\frac{x}{2}\right) + f'(2x - 2y) = (\cos x)\sin(y + 2x) + f(2x - 2y) $$ for all $ x, y \in \mathbb{R} $. If $ f(0) = 1 $, then the value of $ 24f^{(4)}\left(\frac{5\pi}{3}\right) $ is: