33. The simple pendulum in a grandfather clock is 1.0 m long. What are (a) the period and (b) the frequency of this pendulum?
43. (a) If the spring constant in a mass-spring system is tripled, the new period is (1) 3, (2) square root of 3, (3) 1/square root of 3 times the old period. Why?
(b) If the initial period is 2.0 s and the spring constant is halved, what is the new period?
45. In a lab experiment, you are given a spring with a spring constant of 12 N/m. What mass would you suspend on the spring to have an oscillation period of 0.91 s when the mass is in SHM?
51. (a) If a grandfather clock were taken to the Moon, where the acceleration due to gravity is only one-sixth (assume the figure to be exact) that on the Earth, will the period of vibration (1) increase, (2) remain the same, or (3) decrease? Why? (b) If the period on the Earth is 2.0 s, what is the period on the Moon?
63. A longitudinal sound wave has a speed of 340 m/s in air. If this wave produces a tone with a frequency of 1000 Hz, what is its wavelength?
71. In watching a transverse wave go by, a woman in a boat notes that 13 crests pass by in a time of 3.0 s. If she measures the distance between two successive crests to be 0.75 m, and if the first and the last points that pass her are crests, what is the speed of the wave?
75. Fred strikes a train rail with a hammer at a frequency of 0.50 Hz, and Wilma puts her ear to the rail 1.0 km away. (a) How long after the first strike does Wilma hear the sound? (b) What is the time interval between the successive sound pulses she hears?
Please see the attachment for full solutions.
17.a) The position of a particle in harmonic motion can be written as (with no loss of generality):
x(t) = Asin(at + psi)
Where A is the amplitude, ? is the angular frequency and ? is the phase shift. The velocity is the derivative of this expression ...
This solution includes explanation and calculations for each question. 400 words.