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

Click For Summary
SUMMARY

The period of oscillation for an elevator of mass 300 kg suspended by a 96 m long steel cable with a diameter of 3 mm can be calculated using the formula for the period of a simple harmonic oscillator. The string constant (k) is determined using the formula F/A = G * ΔL / L, where F is the force, A is the cross-sectional area, G is the gravitational constant, ΔL is the change in length, and L is the original length of the cable. The correct period is then calculated using the formula T = 2π√(m/k). The initial calculations presented in the discussion were incorrect, necessitating a review of the string constant and period formulas.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with the formula for the period of oscillation
  • Knowledge of material properties, specifically Young's modulus for steel
  • Basic skills in algebra and physics problem-solving
NEXT STEPS
  • Review the derivation of the period formula for simple harmonic oscillators
  • Learn about Young's modulus and its application in calculating string constants
  • Explore the effects of different materials on oscillation periods
  • Investigate real-world applications of oscillation principles in engineering
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of oscillating systems, particularly in the context of structural engineering and earthquake resilience.

phySicNewB
Messages
2
Reaction score
0
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.
 
Last edited:
Physics news on Phys.org
To get help, you must show what you've tried in order to solve the problem. Fill out the rest of the template in your first post.
 

Similar threads

Period of Motion from Equations of Motion
  • · Replies 10 ·
Replies
10
Views
2K
High School Harmonic oscillator and simple pendulum time period
  • · Replies 36 ·
2
Replies
36
Views
4K
How Do You Calculate the Period of Oscillation in a Harmonic Potential?
  • · Replies 2 ·
Replies
2
Views
2K
Rotating simple harmonic oscillator
  • · Replies 11 ·
Replies
11
Views
2K
How to Calculate Amplitude Decrease in Damped Harmonic Motion After 10 Cycles?
  • · Replies 3 ·
Replies
3
Views
996
Harmonic Oscillator and Volume of Unit Cell in Phase Space
  • · Replies 4 ·
Replies
4
Views
4K
Simple Harmonic Oscillator and Damping
  • · Replies 8 ·
Replies
8
Views
3K
How Does a Rod Attached to a Spring Undergo Simple Harmonic Motion?
  • · Replies 3 ·
Replies
3
Views
3K
Equation of motion for isotropic harmonic oscillator
  • · Replies 16 ·
Replies
16
Views
3K
Particle motion when wrapped around drum; elastic string
  • · Replies 8 ·
Replies
8
Views
3K