What is the amplitude of the vertical motion of a segment of the string located at x = 4.000 cm the bridge (the bottom fixed part of the string) is x=0? = 0.4714m 0.000 ou
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.
please help me on number 3 part g the answer I have is wrong.
![3. The C string on a ukulele is fixed at both ends, is 53.34 cm long, and has a linear density of
1.510 x 10-³ kg/m. The string vibrates at the fundamental frequency (first harmonic).
a) What is the longest wavelength that a standing wave on this string can have?
1067m
b) If the fundamental frequency (first harmonic) of this string is 261.6 Hz, what is the speed of the w
along the string?
279.1 m/s
c) What is the tension on the string? F₁ = 117.6 N
d) What is the angular frequency of the wave? w = 1644
s
e) What is the angular wave number of the wave? k = 5890 rom
f)
If the maximum displacement of a small segment of the string at the antinode is 2.560 mm, wri
equation for the displacement (y direction) of any segment of the string as a function of the tim
distance from the end of the string (x direction)? (hint: 2A = 2.560 mm) y = 0.00256 sm (5.8
g) What is the amplitude of the vertical motion of a segment of the string located at x = 4.000 cm
the bridge (the bottom fixed part of the string) is x = 0? = 0.4714m
h) What is the vertical position of the segment of string at x = 4.000 cm at time t = 2.000 s? y
90400
i) What is the second harmonic frequency (n = 2) of this string? ₁₂ 523.2 H 2
j) At the second harmonic, where would you find a node, other than x = 0 cm and x = 53.34
might help to sketch what the second harmonic looks like) o. 2667 m or 26.67](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb8e4727-7fc7-4f82-8a18-069beaabb8fa%2F64d7861c-e859-45a1-8787-192bbd0df47e%2F7atochl_processed.jpeg&w=3840&q=75)
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