Mass on a string-harmonic oscillator

In summary, the conversation discusses a mass on a string problem with a harmonic motion, where the mass of the string is not neglected. The professor wanted to calculate the complete kinetic energy of the system using a formula that takes into account the velocities of different parts of the string. The velocity of the system is expressed as v(x) = A + Bx, which is dependent on parameters such as Young's modulus. The conversation also mentions the need to consider specifications of the string in order to accurately model its behavior.
  • #1
Lushikato
4
0
Hello, I encountered a mass on a string problem in which the mass, moved from the equilibrium, gets a harmonic motion. The catch, however, is that the mass of the string is not neglected. On the lecture, the prof. wanted to calculate, for some reason, the complete kinetic energy of the system:

(1/2)∑mivi2 =(1/2)∫v2dm

where the vi and mi are parts of the string and their velocities. After that, he said that v(x) has the next form:

v(x)=A+Bx

Can anyone elaborate on why the velocity has the dependence written above?
 
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  • #2
It's specified in the question so why worry about it
 
  • #3
It's impossible to model the behavior of the string without knowing some specifications
Like
Young's modulus(and it's variations with velocity, acceleration... Of the string)
However,
Why worry about that as it's altogether a different thing !
 

1. What is a mass on a string-harmonic oscillator?

A mass on a string-harmonic oscillator is a simple physical system that consists of a mass attached to a string or spring and allowed to oscillate back and forth due to the force of gravity or other external forces.

2. What is the equation for the motion of a mass on a string-harmonic oscillator?

The equation for the motion of a mass on a string-harmonic oscillator is given by x(t) = Asin(ωt + φ), where x is the displacement of the mass, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

3. How does the amplitude affect the motion of a mass on a string-harmonic oscillator?

The amplitude of a mass on a string-harmonic oscillator determines the maximum displacement of the mass from its equilibrium position. A larger amplitude results in a larger displacement and a higher energy of the system, causing it to oscillate with a greater speed.

4. What factors affect the period of a mass on a string-harmonic oscillator?

The period of a mass on a string-harmonic oscillator is affected by the length of the string or the stiffness of the spring, the mass of the object, and the force acting on the mass. The period is longer for longer strings or stiffer springs, larger masses, and weaker forces.

5. What is the relationship between the frequency and period of a mass on a string-harmonic oscillator?

The frequency and period of a mass on a string-harmonic oscillator are inversely proportional. This means that as the frequency increases, the period decreases and vice versa. The frequency is equal to the inverse of the period, or f = 1/T, where f is the frequency and T is the period.

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