Question

Explain why the resonance frequency is a double of the driven frequency of the signal generator.

Answer 1

ans)

Connect the signal generator output to the EXT COUNTER input terminal as well as the amplifier's input terminals. When the instrument is set to the EXT COUNTER function, then the frequency meter counts the number of cycles of oscillation in a fixed time interval and displays the result as a frequency reading.

Even when the driving frequency exactly matches the resonance frequency, then it may take a few seconds to establish this resonating vibration.

When resonance has been found, reduce the amplitude of the driving signal and carefully repeat the search near the same frequency.

Resonance occurs when an LC circuit is driven from an external source at an angular frequency ₀ at which the inductive and capacitive reactances are equal in magnitude. This is called as the "resonant frequency".

The resonant frequency of LC circuit is given as -

₀ = 1 / L C

where, L = inductance & C = capacitance

Therefore, an equivalent frequency will be given as -

f₀ = ₀ / 2

f₀ = 1 / 2 L C

We know that,

Driving frequency is the frequency of a driving force. When the oscillating system starts oscillating on its own at a frequency (f₀), then this frequency is called as "resonance frequency". A system oscillating due to an external excitation with a frequency (f_ext), then this frequency is called as "driving frequency".