A physics club wants to build a large pendulum that will swing in step with the ticking of a metronome that beats 120 times per minute.
(a) Compute the length that the pendulum should have so that it resonates with the metronome beats. Take g=9.8ms−2 and assume small–angle oscillations.
(b) If the pendulum bob is replaced by another bob of five times the mass but the length is kept the same, state with reason whether the resonance condition with the metronome is still satisfied.
(c) Suppose due to a loose clamp the effective length of the pendulum decreases by 2%. Estimate the new natural period and comment on the extent to which resonance with the metronome will be affected.