PLEASE EXPLAIN ALL ANSWERS FROM 13-20 During an earthquake on May 12. 2008, the

Question

PLEASE EXPLAIN ALL ANSWERS FROM 13-20

During an earthquake on May 12. 2008, the Tuned-Mass-Damper assembly at top of the "I" Taipei 101 Tower was found to oscillate with large amplitude A = 1.2 m. The period of oscillation was found to be T = 2 seconds Calculate the angular frequency of the motion Calculate the kinetic energy of the mass in problem 13, knowing that it weighs 660 metric tons (1 metric ton = 1000 kg) In problem 16, find the period of his motion. The A string of a cello vibrates at frequency f = 220 Hz in its 1s normal mode (fundamental mode). The vibrating string is 70 cm long and has a mass of g. Find the tension in the string. Using the information in problem 19, determine the frequency when the strin has two antinodes.

Explanation / Answer

13)
angular frequency, w = (2* pi)/ T = pi = 3.14 radian/s is the answer
14)
velocity = A* w = 1.2 * 3.14 = 3.8 m/s
15)
Kinetic energy = 0.5 * m* v^2 = 0.5 * 660 * 1000 * 3.8^2 = 4.8 * 10^6 J
16)
w = 6.28 rad/s
17)
T = 1 sec
18)
v = 33.9 m/s
19)
wavelength = 2* length = 2* 0.7 = 1.4 m
velocity = wavelength * frequency = 1.4 * 220 = 308 m/s
we have , v = sqrt ( T/ (m/L))
308 = sqrt ( T / (0.0012/0.7))
T = Tension = 161.3 N
20)
when string has 2 antinodes, wavelength = 0.7 m
so, frequency = velocity / wavelength = 308/0.7 = 440 Hz is the answer

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.