A simple pendulum is fitted with a small electromagnet that delivers a horizontal periodic driving force of adjustable frequency while the damping is negligibly small. The length of the pendulum is 0.90m.
(i) Calculate the natural frequency (in Hz) of small oscillations of the pendulum.
(ii) The driving frequency is slowly varied until resonance is obtained. Find the driving frequency at which resonance occurs.
(iii) If the driving frequency is increased by 10% above the resonant value, explain qualitatively how the amplitude of steady oscillations will change. State whether it increases, decreases, or remains the same, and give a reason.