Energy of Oscillations: Find Work Done Against Tension

Click For Summary
SUMMARY

The discussion focuses on calculating the energy of oscillations in a string clamped at both ends, pulled up a distance h with tension T. The key equation used is E=K+U, where K represents kinetic energy and U represents potential energy. Participants emphasize the importance of determining the force required to maintain a small displacement y and integrating this force from y=0 to y=h to find the work done against tension. The conversation highlights common pitfalls, such as miscalculating factors of 2 in the equations.

PREREQUISITES
  • Understanding of basic mechanics, specifically tension in strings.
  • Familiarity with energy concepts, including kinetic and potential energy.
  • Ability to perform integration, particularly in the context of physics problems.
  • Knowledge of small angle approximations in physics.
NEXT STEPS
  • Study the derivation of energy equations in oscillating systems.
  • Learn about tension forces in strings and their implications in wave mechanics.
  • Explore integration techniques used in physics, especially for calculating work done.
  • Review small angle approximation applications in various physics scenarios.
USEFUL FOR

Students studying mechanics, physics educators, and anyone interested in understanding the dynamics of oscillating systems and energy calculations in strings.

anubis01
Messages
149
Reaction score
1

Homework Statement


A string of length L is clamped at both ends, pulled up a distance h with tension T. What is the energy of the subsequent oscillations after plucking. [Hint, consider the work done against the tension in giving the string its initial deformation]


Homework Equations


E=K+U


The Attempt at a Solution


I'm not completely sure if my answer is correct or not, so if anyone can help me check it I would greatly appreciate it. I also just scanned my work because I'm not that great at using the forums latex commands.

http://img242.imageshack.us/img242/1155/cci24092009800000i.jpg
 
Last edited by a moderator:
Physics news on Phys.org
That seems to be correct.

In order to use the hint, you first need to figure out what is the force required to hold the string at a (small) displacement y (using small angle approximations). Then, the work is the integral of this force from y=0 to y=h. Doing this, you will get the same answer.

BTW, good job with all those pesky factors of 2. I always screw those up.
 
turin said:
That seems to be correct.

BTW, good job with all those pesky factors of 2. I always screw those up.

yeah those factors of 2 tricked me up for a while too. Thanks for the help, its much appreciated.
 

Similar threads

High School Curious about the work - energy theorem
  • · Replies 8 ·
Replies
8
Views
2K
Energy of Oscillations in Clamped String of Tension T
  • · Replies 9 ·
Replies
9
Views
4K
Tension Force Problem (applying Work-Kinetic Energy Theorem)
  • · Replies 16 ·
Replies
16
Views
1K
Small oscillations and a time dependent electric field
  • · Replies 4 ·
Replies
4
Views
2K
Calculating Total Energy of Vibration for a String
  • · Replies 1 ·
Replies
1
Views
6K
MATLAB Code: Stationary Schrodinger EQ, E Spec, Eigenvalues
  • · Replies 1 ·
Replies
1
Views
3K
Micro Spring (DNA): Determine Energies, Find Expected Length
  • · Replies 2 ·
Replies
2
Views
2K
Transverse Oscillations with 3 beads
  • · Replies 3 ·
Replies
3
Views
2K
3D Harmonic Oscillator - Eigenfunctions and Eigenvalues
  • · Replies 6 ·
Replies
6
Views
5K
High School Curious about Work and Energy Consumption
  • · Replies 8 ·
Replies
8
Views
2K