The equation of an S.H.M. with amplitude A an | vedclass

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(D) Let the two extreme positions be $x = 0$ and $x = 2A$. At $t = 0$,the particle is at the 'other' extreme position. Let this be $x = 2A$. The gener

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$x = A + A \cos \omega t$

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(D) Let the two extreme positions be $x = 0$ and $x = 2A$. At $t = 0$,the particle is at the 'other' extreme position. Let this be $x = 2A$. The general equation for $S.H.M.$ is $x' = A \cos(\omega t + \phi)$,where $x'$ is measured from the mean position $x = A$. Thus,$x - A = A \cos(\omega t + \phi)$. At $t = 0$,$x = 2A$,so $2A - A = A \cos(\phi) \implies A = A \cos(\phi) \implies \cos(\phi) = 1 \implies \phi = 0$. Substituting $\phi = 0$ into the equation: $x - A = A \cos(\omega t) \implies x = A + A \cos(\omega t)$.

The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...

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