(i) Define the natural frequency of a mechanical oscillator.
(ii) A small block of mass m is suspended from a light vertical spring of force constant k and set into small vertical oscillations. Explain, without explicit calculation, how the natural angular frequency of oscillation will change in the following independent situations:
(a) the mass is doubled while the spring constant remains the same,
(b) the spring constant is quadrupled while the mass remains the same.
(iii) Using your qualitative answers to part (ii), state by what factor the natural linear frequency will change in case (b). Give a brief reason for your answer.