Pendulums and Wave Speed in Strings
pg 442-445 #26, 33, 50(a,b), 78, 79, 91

26. If pendulum A has a period twice that of pendulum B, then
     (a) L₁ = 2L₂ and m₁ = ½m₂
     (b) L₁ = 2L₂ and m₁ = 2m₂
     (c) L₁ = 2L₂ regardless of mass
     (d) none of the preceding.

33. Students use a pendulum with a length of 36.90 cm to measure the acceleration of gravity at the location of their school. If the period of the pendulum is found to be 1.220 s, what is the approximate value of g?

50. A grandfather clock has a pendulum that is 75.00 cm long. It is accidentally broken, and when repaired the length is shorter by 2.0 mm. Considering the clocks pendulum to be a simple pendulum (a) will the repaired clock gain or lose time? (b) By how much will he repaired clock differ from the correct time (taken to be the time determined by the original pendulum in 24 hr)? 

78. A father pushes a 25 kg child on a swing. If the length of the swing is 3.0 m, how often does the father have to push to drive the system in resonance (that is, to keep the child swinging with higher and higher amplitude)? Does the mass of the child really make any difference?

79. A piece of rubber tubing with a linear mass density of 0.125 kg/m is stretched by a force of 9.00 N (a) What will be the wave speed along the tubing? (b) If the stretched tubing has a length of 10.0 m, what is its natural fundamental frequency?

91. A pendulum makes 6.0 complete cycles in a time of 10 seconds. What are the frequency and period of the pendulum's oscillation?