Given below are two statements. One is labell | vedclass

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(D) For a simple harmonic motion,the position is given by $x(t) = A \sin(\omega t + \phi)$.At $t = 0$,$x_0 = A \sin \phi$  $..........(1)$The momentum

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Both $(A)$ and $(R)$ are true and $(R)$ is the correct explanation of $(A)$.

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(D) For a simple harmonic motion,the position is given by $x(t) = A \sin(\omega t + \phi)$.At $t = 0$,$x_0 = A \sin \phi$  $..........(1)$The momentum is $p(t) = m \frac{dx}{dt} = m A \omega \cos(\omega t + \phi)$.At $t = 0$,$p_0 = m A \omega \cos \phi$  $..........(2)$From equations $(1)$ and $(2)$,we can solve for the two unknowns,amplitude $A$ and phase constant $\phi$,using the initial conditions $x_0$ and $p_0$.Specifically,$	an \phi = \frac{m \omega x_0}{p_0}$ and $A = \sqrt{x_0^2 + (p_0 / m \omega)^2}$.Since $A$ and $\phi$ are uniquely determined by $x_0$ and $p_0$,the state of the system at any time $t$ is fully determined.Thus,both Assertion $(A)$ and Reason $(R)$ are true,and $(R)$ is the correct explanation of $(A)$.

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