Two simple pendulums P and Q are set up side by side. The length of Q is four times the length of P(LQ=4LP). Both pendulums oscillate with small amplitudes at the same place where g=9.8m s−2.
(a) Derive the ratio of their angular frequencies ωP:ωQ.
(b) If pendulum Q completes 150 oscillations in a certain time interval, how many oscillations does pendulum P complete in the same interval?
(c) Given LP=0.50m, calculate the difference in the time taken by the two pendulums to complete 60 oscillations each.