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.
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.
University Physics Volume 1
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Chapter15: Oscillations
Section: Chapter Questions
Problem 60AP: A mass is placed on a frictionless, horizontal table. A spring (k=100N/m) , which can be stretched...
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Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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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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