Final answer:
The question asks to solve a trigonometric equation for the variable ω₀. Standard algebraic methods are not easily applicable due to the inverse tangent functions, and numerical methods or graphing tools may be necessary to find the solution.
Step-by-step explanation:
The equation given is -125 = tan⁻¹ (ω₀/s3) - tan⁻¹ (ω₀/5300) - tan⁻¹ (ω₀/10000). This is a trigonometric equation that needs to be solved for the variable ω₀. The difficulty in this equation is that it involves inverse tangent functions, which do not have straightforward algebraic solving methods. Solving this kind of equation typically requires iterative numerical methods or a graphing approach to find the value of ω₀ that satisfies the equation. It might involve using computing tools such as scientific calculators or computer algebra systems that can handle inverse trigonometric functions.