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A string of length 8 m, which has a total mass of 5 g, is stretched along the x-axis and put under a tension of 9 N. One end of the string is attached to a simple harmonic oscillator that is fixed in place at x = 0 but free to move in the ty direction. The maximum displacement of the oscillator is 3 cm above or below the x-axis, and it completes 60 cycles every second. At time t = 0, the oscillator is at y = -3 cm. (a) Write the wave function y(x, t) for the vertical displacement of particles along the string. (b) Obtain an expression for the mechanical energy per unit length of the string, dEter/dx, as a function of x and t. Integrate this along the length of the string to find its total energy content, at a fixed time to. Compare your answer to the value of Mw?A², where M is the total mass of the string.

A string of length 8 m, which has a total mass of 5 g, is stretched along the x-axis and put under a tension of 9 N. One end of the string is attached to a simple harmonic oscillator that is fixed in place at x = 0 but free to move in the ty direction. The maximum displacement of the oscillator is 3 cm above or below the x-axis, and it completes 60 cycles every second. At time t = 0, the oscillator is at y = -3 cm. (a) Write the wave function y(x, t) for the vertical displacement of particles along the string. (b) Obtain an expression for the mechanical energy per unit length of the string, dEter/dx, as a function of x and t. Integrate this along the length of the string to find its total energy content, at a fixed time to. Compare your answer to the value of Mw?A², where M is the total mass of the string.

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A string of length 8 m, which has a total mass of 5 g, is stretched along the x-axis and put under a tension of 9 N. One end of the string is attached to a simple harmonic oscillator that is fixed in place at x = 0 but free to move in the ty direction. The maximum displacement of the oscillator is 3 cm above or below the x-axis, and it completes 60 cycles every second. At time t = 0, the oscillator is at y = -3 cm. (a) Write the wave function y(x, t) for the vertical displacement of particles along the string. (b) Obtain an expression for the mechanical energy per unit length of the string, dEter/dx, as a function of x and t. Integrate this along the length of the string to find its total energy content, at a fixed time to. Compare your answer to the value of Mw²A?, where M is the total mass of the string.
Transcribed Image Text:A string of length 8 m, which has a total mass of 5 g, is stretched along the x-axis and put under a tension of 9 N. One end of the string is attached to a simple harmonic oscillator that is fixed in place at x = 0 but free to move in the ty direction. The maximum displacement of the oscillator is 3 cm above or below the x-axis, and it completes 60 cycles every second. At time t = 0, the oscillator is at y = -3 cm. (a) Write the wave function y(x, t) for the vertical displacement of particles along the string. (b) Obtain an expression for the mechanical energy per unit length of the string, dEter/dx, as a function of x and t. Integrate this along the length of the string to find its total energy content, at a fixed time to. Compare your answer to the value of Mw²A?, where M is the total mass of the string.
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