Energy of Oscillations: Find Work Done Against Tension

Have a good day!In summary, the problem involves a string of length L clamped at both ends and pulled up a distance h with tension T. The energy of the subsequent oscillations after plucking can be determined by considering the work done against the tension in giving the string its initial deformation. Using small angle approximations, the force required to hold the string at a small displacement y can be found and integrated from y=0 to y=h to calculate the work. This method yields the same answer as the original approach.
  • #1
anubis01
149
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
 
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  • #2
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.
 
  • #3
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.
 

1. What is the definition of energy of oscillations?

The energy of oscillations refers to the total amount of energy present in a system undergoing periodic motion, such as a pendulum or a spring. It includes both kinetic energy, which is the energy of motion, and potential energy, which is the energy stored in the system due to its position.

2. How is the energy of oscillations calculated?

The energy of oscillations can be calculated using the equation E = 1/2 * k * x^2, where E is the energy, k is the spring constant, and x is the displacement from equilibrium. This equation applies to systems that exhibit simple harmonic motion, where the restoring force is directly proportional to the displacement.

3. What is the relationship between work done against tension and energy of oscillations?

The work done against tension is directly related to the energy of oscillations. As the system oscillates, the tension in the spring or string changes, and work is done against this tension to maintain the motion. This work is converted into potential energy, which contributes to the overall energy of oscillations.

4. How does the amplitude affect the energy of oscillations?

The amplitude, or maximum displacement, of the oscillating system has a direct impact on the energy of oscillations. As the amplitude increases, so does the energy, since the displacement is squared in the energy equation. This means that larger amplitudes result in greater energy of oscillations.

5. Can the energy of oscillations ever be negative?

No, the energy of oscillations can never be negative. This is because energy is a scalar quantity and is always positive. However, the energy can decrease if there is an external force acting on the system, such as friction or air resistance, which dissipates the energy as heat. In this case, the energy of oscillations would decrease over time.

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