A thin rod of mass M = 10.0 kg and length L = 60.0 cm is connected to a wall by a hinge. A rope of mass m = 40.0 g and length l = 1.00 m is attached to the end of the rod as shown in the image. Assume that when the rope is disturbed, the rod remains relatively stationary without significant "jiggle". a) If the rope is plucked to produce the lowest-frequency standing wave, what is the resonant frequency of this wave (first harmonic)? b) Let A = 10.0 cm represent the amplitude of the standing wave, defined as the maximum displacement from equilibrium of the point on the rope with the largest oscillations. The displacement y of this point as a function of time can be expressed as y = A sin wt, where w is the angular frequency. What is the maximum velocity of this point during its oscillations? c) Assume you manage to get the second harmonic on the same string, which points) on the rope have an amplitude of 10.0 cm? Draw a picture or write as distance from the hinge. Justify answer.
A thin rod of mass M = 10.0 kg and length L = 60.0 cm is connected to a wall by a
hinge. A rope of mass m = 40.0 g and length l = 1.00 m is attached to the end of the
rod as shown in the image. Assume that when the rope is disturbed, the rod remains relatively stationary without significant "jiggle".
a) If the rope is plucked to produce the lowest-frequency standing wave, what is the resonant frequency of this wave (first harmonic)?
b) Let A = 10.0 cm represent the amplitude of the standing wave, defined as the
maximum displacement from equilibrium of the point on the rope with the largest oscillations. The displacement y of this point as a function of time can
be expressed as y = A sin wt, where w is the angular frequency. What is the
maximum velocity of this point during its oscillations?
c) Assume you manage to get the second harmonic on the same string, which points) on the rope have an amplitude of 10.0 cm? Draw a picture or write as distance from the hinge.
Justify answer.
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