how to Find the spring constant k and the mass m, can anyone help please.

Question

The natural frequency of a spring-mass system is found to be 2 Hz. When an additional

mass of 1 kg is added to the original mass m, the natural frequency is reduced to 1 Hz. Find

the spring constant k and the mass m.

Answer 1

T₁ = 2π√m/k; T₂ = 2π√(m + 1)/k; T₁/T₂ = √m/(m+ 1); m /(m + 1) = f₂²/f₁² = 1/4; 4m = m + 1; 3m = 1; m = 1/3 kg