A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left end of the string is connected to a massless ring that slides on a frictionless pole, and the ring is attached to a spring of stiffness 150 N/m. The right end is attached to a massless ring that slides on a frictionless pole. The left end of the string is driven by a transverse force of amplitude 4.0N and frequency 21 Hz. F(t) x = 0 x = L 2. The input mechanical impedance (at x = 0) is Zmo = s/im + ipLc tan(kL). Using established impedances (do not calculate), explain why the input impedance is given by this expression. Evaluate the impedance for the specified values of the system. Be sure to show the units. Note: In the computation of the tangent, do not round off the value of k. From the value of the impedance, determine the steady-state velocity amplitude (in m/s) of the left ring.

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Chapter13: Vibrations And Waves
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Problem 32P: A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is...
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A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left
end of the string is connected to a massless ring that slides on a frictionless pole,
and the ring is attached to a spring of stiffness 150 N/m. The right end is attached
to a massless ring that slides on a frictionless pole. The left end of the string is
driven by a transverse force of amplitude 4.0 N and frequency 21 Hz.
F(t)
S
x = 0
x = L
2. The input mechanical impedance (at x = 0) is Zmo = s/im + ipLc tan(kL). Using
established impedances (do not calculate), explain why the input impedance is
given by this expression. Evaluate the impedance for the specified values of the
system. Be sure to show the units. Note: In the computation of the tangent, do
not round off the value of k. From the value of the impedance, determine the
steady-state velocity amplitude (in m/s) of the left ring.
Transcribed Image Text:A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left end of the string is connected to a massless ring that slides on a frictionless pole, and the ring is attached to a spring of stiffness 150 N/m. The right end is attached to a massless ring that slides on a frictionless pole. The left end of the string is driven by a transverse force of amplitude 4.0 N and frequency 21 Hz. F(t) S x = 0 x = L 2. The input mechanical impedance (at x = 0) is Zmo = s/im + ipLc tan(kL). Using established impedances (do not calculate), explain why the input impedance is given by this expression. Evaluate the impedance for the specified values of the system. Be sure to show the units. Note: In the computation of the tangent, do not round off the value of k. From the value of the impedance, determine the steady-state velocity amplitude (in m/s) of the left ring.
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