The Electrical-Mechanical Analogy — Question 2

Question 2

Matching a mechanical time scale does not require matching its units

A mechanical oscillator has m=.600 kg and k=150 N/m. An electrical analogue is to use L=.0800 H and have the same natural angular frequency.

1. Find the required capacitance.

2. Compare the effect of doubling mechanical mass with doubling electrical inductance.

Question 2 - Solution

Matching a mechanical time scale does not require matching its units

(a) Method and calculation

$$\omega^2=k/m=250\,s^{-2}=1/(LC).$$$$\boxed{C=m/(kL)=.0500\,F}.$$

(b) Interpretation and further calculation

$$\omega_m\propto m^{-1/2},\quad\omega_e\propto L^{-1/2}.$$$$\boxed{\omega_{\mathrm{new}}/\omega_{\mathrm{old}}=1/\sqrt2\quad\text{in both cases}}.$$

Physical check

Corresponding coefficients have different physical units but the same role in the differential equation.