How to change the frequency of free oscillations in the circuit, if the inductance decreases by 2 times

How to change the frequency of free oscillations in the circuit, if the inductance decreases by 2 times, and the capacitance increases by 8 times?

Given:
L₁ = 2L₂,
C₂ = 8C₁.
To find:
v-?
Decision:
ν = 1 / T = 1 / 2π√LC,
ν₂ / ν₁ = √L₁C₁√ / L₂C₂ = √ (2 * L₂ * C₁ / 8 * L₂ * C₁) = √1 / 4 = 1/2,
that is, ν₂ = ν₁ / 2
Answer: will decrease by 2 times.



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