Initial displacement of a midpoint of a string?

In summary, the initial displacement of a midpoint of a string refers to the starting position of the midpoint of the string when it is plucked or struck. It is typically measured in meters or centimeters and can be affected by factors such as force, tension, stiffness, length, and thickness of the string. It is not the same as amplitude and is important in determining the behavior and characteristics of the string's motion, particularly in stringed instruments.
  • #1
Howard Fox
38
2

Homework Statement


upload_2018-11-15_10-59-9.png

Then we are asked to determine the initial discplament, velocity and acceleration of the midpoint of the string.

Homework Equations


I guess we should use equation x(t)=Asin(wt+phi)

The Attempt at a Solution


My attempted solution is to use the above equationa and put t=0. That would give us an initial displacement of 1.60x10^-3 m, and for the velocity and acceleration differentiate the initial equation and again put t=0.
Is that a good solution? Thank you
 

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  • #2
That is perfect.
 

Related to Initial displacement of a midpoint of a string?

1. What is the initial displacement of a midpoint of a string?

The initial displacement of a midpoint of a string refers to the starting position of the midpoint of a string when it is plucked or struck. It is the distance from the equilibrium position of the string to the midpoint at the beginning of the motion.

2. How is the initial displacement of a midpoint of a string measured?

The initial displacement of a midpoint of a string is typically measured in meters or centimeters. It can be measured using a ruler or other measuring device by determining the distance from the equilibrium position to the midpoint of the string.

3. What factors affect the initial displacement of a midpoint of a string?

The initial displacement of a midpoint of a string can be affected by a variety of factors, including the force used to pluck or strike the string, the tension of the string, and the stiffness of the string. It can also be affected by the length and thickness of the string.

4. Is the initial displacement of a midpoint of a string the same as the amplitude?

No, the initial displacement of a midpoint of a string is not the same as the amplitude. The amplitude refers to the maximum displacement of the string from its equilibrium position during its motion, while the initial displacement refers to the starting position of the string.

5. Why is the initial displacement of a midpoint of a string important?

The initial displacement of a midpoint of a string is important because it affects the behavior and characteristics of the string's motion. It can impact the frequency, wavelength, and other properties of the string's vibrations, and is a key factor in understanding and analyzing the behavior of stringed instruments such as guitars and violins.

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