During an earthquake a skyscraper is designed to sway back and forth with simple harmonic motion?
ID: 2115534 • Letter: D
Question
During an earthquake a skyscraper is designed to sway back and forth with simple harmonic motion with a period of 8 seconds. The amplitude at the top floor for a particular earthquake is 70 cm. With respect to the simple harmonic motion to the top floor, calculate the following quantities:A) The radius of the circle used to represent the SHM.
B) The speed of the object moving around the circle.
C) The angular velocity.
D) The maximum speed of the top floor. PLEASE SHOW WORK During an earthquake a skyscraper is designed to sway back and forth with simple harmonic motion with a period of 8 seconds. The amplitude at the top floor for a particular earthquake is 70 cm. With respect to the simple harmonic motion to the top floor, calculate the following quantities:
A) The radius of the circle used to represent the SHM.
B) The speed of the object moving around the circle.
C) The angular velocity.
D) The maximum speed of the top floor. PLEASE SHOW WORK
Explanation / Answer
A)
radius = 70 cm
b)
speed = 0.7*2*3.14/8 = 0.5495 m/s
c)
angular vel = 0.5495/0.7 = 0.785 rad/s
d)
max speed = 0.5495 m/s
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