The new natural frequency would be ω/2.
we know that,
[tex]f = \frac{1}{2 pi \sqrt{LC} }[/tex] = ω. -> equation 1
now, when capacitance is quadrupled,
[tex]f' = \frac{1}{2 pi \sqrt{L ( 4C )} }[/tex]
[tex]f' = \frac{1}{2 pi (2)\sqrt{LC} }[/tex]. -> equation 2
substituting value of equation 1 in equation 2 , we get,
[tex]f' = \frac{w}{2}[/tex]
Hence, the new natural frequency of the circuit is ω/2.
what do you mean by frequency ?
The resonant frequency for a particular circuit is the frequency at which this equality stands true. Where L is the inductance in henries and C is the capacitance in farads, this is the LC circuit's resonant frequency.
Learn more about frequency here:-
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