Finding the Period of Oscillation for an Elevator After a Minor Earthquake

In summary, the conversation discussed the oscillation of an elevator after a minor earthquake. The elevator has a mass of 300 kg and is suspended by a long, thin steel cable with a length of 96 m and diameter of 3 mm. The speaker attempted to find the period of oscillation by using the formula F/A=G*Delta length/length of the cable to find the string constant, and then using the formula period=2pie*square root of mass/string constant. However, the answer did not match the expected result.
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An elevator of mass M = 300 kg hangs at the end of a long, thin steel cable: it has length L = 96 m and diameter d = 3 mm.

A minor earthquake shakes the entire building. After the quake passes, the elevator continues to bob up and down for a long time. What is the period of oscillation?
i used F/A=G*Delta length/length of the cable to find the string constant. ..then i used period=2pie*square ROOt of mass/string constant to find period...however, the answer is no right.
 
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1. What is elevator harmonic motion?

Elevator harmonic motion is the repetitive movement of an elevator up and down, caused by the imbalance of forces acting on it. Specifically, it is a type of simple harmonic motion, where the elevator moves back and forth between two points with a constant period and amplitude.

2. What factors affect elevator harmonic motion?

The factors that affect elevator harmonic motion include the weight of the elevator and its passengers, the tension in the cable, and the gravitational force. The speed of the elevator can also impact the motion, as well as external forces such as wind or earthquakes.

3. How is elevator harmonic motion calculated?

The equation for calculating elevator harmonic motion is T = 2π√(m/k), where T is the period of the motion, m is the mass of the elevator and its passengers, and k is the spring constant of the cable. This equation is derived from Hooke's law, which states that the force exerted by a spring is proportional to its displacement.

4. What are the practical applications of elevator harmonic motion?

Elevator harmonic motion has several practical applications, including in the design and operation of elevators and amusement park rides. It is also used in the study of vibration and oscillation in mechanical engineering, as well as in seismology to measure the effects of earthquakes.

5. How is elevator harmonic motion related to energy?

Elevator harmonic motion follows the law of conservation of energy, where the total energy of the system remains constant. As the elevator moves up and down, the potential energy is converted into kinetic energy and back again, with the total energy remaining the same. This principle is important in understanding the stability and efficiency of elevator systems.

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