In the circuit shown switches \( S_{1} \) and \( S_{3} \) have been closed forș1 sec and \( S_{2...

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In the circuit shown switches \( S_{1} \) and \( S_{3} \) have been closed forș1 sec and \( S_{2} \) remained open. Just after 1 second is over switch \( S_{2} \) is closed and \( S_{1}, S_{3} \) are opened.

The charge on the upper plate of the capacitor as function of time taking the instant of switching on of \( S_{2} \) and switching off all the switches to be \( t=0 \) is \( q=x \times 10^{-2} \cos \left(t+\frac{\pi}{4}\right) \).
Find out value of \( x \). (Given \( \left.\left(1-\frac{1}{e}\right) \sqrt{2} \cong 0.89\right) \)
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