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Determine whether the following systems are time invariant or not, $y(t)=x(t) \sin w t$
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Solution:

Output due to input delayed by T seconds,

$y(t, T)=x(t-T) \sin w t$

Output delayed by T seconds,

$ \begin{gathered} y(t-T)=x(t-T) \sin w(t-T) \\\\ \because y(t, T) \neq y(t-T)\\ \end{gathered} \\ $

The given system is time-variant.

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