Hwk89B_combination

# Hwk89B_combination - 0 m s Take the origin at the left end...

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PHYS 153 Homework 8B Problem 1 A 2 . 20 kg mass oscillates on a spring of force constant 250 . 0 N / m with a period of 0 . 615 s. (a) Is this system damped or not? How do you know? If it is damped, ﬁnd the damping constant b . (b) Is the system undamped, underdamped, critically damped, or overdamped? How do you know? Problem 2 a transverse wave on a rope is given by y ( x, t ) = (0 . 750 cm) cos π ±( 0 . 400 cm - 1 ) x + ( 250 s - 1 ) t ² (a) Find the amplitude, period, frequency, wavelength, and speed of propagation. (b) Sketch the shape of the rope at these values of t : 0 , 0 . 0005 s , 0 . 0010 s. (c) Is the wave trav- eling in the + x - or - x -direction? (d) The mass per unit length of the rope is 0 . 0500 kg / m. Find the tension. (e) Find the average power of this wave. Problem 3 A transverse sine wave with an amplitude of 2 . 50 mm and a wavelength of 1 . 80 m travels from left to right along a long, horizontal, stretched string with a speed of 36
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Unformatted text preview: . 0 m / s. Take the origin at the left end of the undisturbed string. At time t = 0 the left end of the string has its maximum upward displacement. (a) What are the frequency, angular frequency, and wave number of the wave? (b) What is the function y ( x, t ) that describes the wave? (c) What is y ( t ) for a particle at the left end of the string? (d) What is y ( t ) for a particle 1 . 35 m to the right of the origin? (e) What is the maximum magnitude of transverse velocity of any particle of the string? (f) Find the transverse displacement and the transverse velocity of a particle 1 . 35 m to the right of the origin at time t = 0 . 0625 s. 1 - 1...
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