A horizontal spring–mass system executes simple harmonic motion on a frictionless table. The mass attached to the spring can be varied while the same spring is used throughout the experiment.
(i) State the mathematical expression for the time period T of oscillation of a body of mass m attached to a spring of force constant k.
(ii) Using the expression in part (i), show how the time period changes when (a) the mass is doubled while the same spring is used, and (b) the spring is replaced by another whose force constant is four times larger while the mass remains the same.
(iii) Explain physically why increasing the inertial factor (mass) has the opposite effect on the time period compared with increasing the restoring factor (spring constant).