### Related Formula The general solution tracking position in SHM is given by : x(t) = A sin(omega t + phi)$x(t) = A \sin(\omega t + \phi)$ Momentum formula: p(t) = m v(t) = m A omega cos(omega t + phi)$p(t) = m v(t) = m A \omega \cos(\omega t + \phi)$ ### Core Logic At t = 0$t = 0$ : 1) x_0 = A sin phi$x_0 = A \sin \phi$ 2) p_0 = m A omega cos phi$p_0 = m A \omega \cos \phi$ Dividing equation (1) by (2) reveals the phase \angle relationship : tan phi = left(fracx_0p_0right) m omega implies phi = tan^-1left(fracm omega x_0p_0right)$\tan \phi = \left(\frac{x_0}{p_0}\right) m \omega \implies \phi = \tan^{-1}\left(\frac{m \omega x_0}{p_0}\right)$ Squaring and combining both equations isolates amplitude A$A$: A = fracsqrt(m omega x_0)^2 + p_0^2m omega$A = \frac{\sqrt{(m \omega x_0)^2 + p_0^2}}{m \omega}$ Since both amplitude A$A$ and phase constant phi$\phi$ are explicitly fixed by the initial conditions x_0$x_0$ and p_0$p_0$, the kinematic layout of the state space is completely specified for any future time parameter t$t$. This validates that Reason (R) perfectly explains Assertion (A). ### Pattern Recognition SHM is a second-order differential equation. Any system of second-order equations requires exactly two independent boundary conditions (e.g., initial position and velocity/momentum) to completely specify unique path tracks. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Oscillations