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2. The total energy E,(kınetic + potential) = mwž (Af + B; )/4 of a normal mode may be found by an alternatıve method, where each section dr of the string is treated as a sımple harmonic oscillator with the total energy cqual to the maxımum kınetue energy of oscillation k. emax = pdx(y;)max =pdxwž(})max If the value of (y)max at a point x on the string is given by G)max = (Až + Bž ) sın * (a) Show that the sum of the energies of the osciıllators along the string, that 1s, the integral gives the expected result (b) What is the implıcation of the result on the conversation of energy? (Note, the normal freguency w. = nnc/l.)

2. The total energy E,(kınetic + potential) = mwž (Af + B; )/4 of a normal mode may be found by an alternatıve method, where each section dr of the string is treated as a sımple harmonic oscillator with the total energy cqual to the maxımum kınetue energy of oscillation k. emax = pdx(y;)max =pdxwž(})max If the value of (y)max at a point x on the string is given by G)max = (Až + Bž ) sın * (a) Show that the sum of the energies of the osciıllators along the string, that 1s, the integral gives the expected result (b) What is the implıcation of the result on the conversation of energy? (Note, the normal freguency w. = nnc/l.)

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Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? % Cut A Find - Calibri (Body) - 11 - A A Aa AaBbCcDc AaBbCcD AaBbC AaBbCc AaBI AqBbCcl E Copy a Replace Paste B I U - abe x, x I Normal I No Spaci.. Heading 1 Change Styles Heading 2 Title Subtitle A Select - Format Painter Clipboard Font Paragraph Styles Editing L 2. The total energy E„(kınetic + potential) = mw; (AR + B; )/4 of a normal mode may be found by an alternative method, where each section dx of the string is treated as a sımple harmonic oscillator with the total energy equal to the maximum kınetic energy of oscillation k. emax =5 pdx(y)max = If the value of (y)max at a point x on the string is given by G)max = (A + B3 ) sın? Onx (a) Show that the sum of the energies of the oscillators along the string, that is, the integral gives the expected result (b) What is the implication of the result on the conversation of energy? (Note. the normal frequency wn = NITC/l.) ll 12:33 PM 2021-09-20 Page: 1 of 1 B I E E E 90% e Words: 0 +
Transcribed Image Text:Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? % Cut A Find - Calibri (Body) - 11 - A A Aa AaBbCcDc AaBbCcD AaBbC AaBbCc AaBI AqBbCcl E Copy a Replace Paste B I U - abe x, x I Normal I No Spaci.. Heading 1 Change Styles Heading 2 Title Subtitle A Select - Format Painter Clipboard Font Paragraph Styles Editing L 2. The total energy E„(kınetic + potential) = mw; (AR + B; )/4 of a normal mode may be found by an alternative method, where each section dx of the string is treated as a sımple harmonic oscillator with the total energy equal to the maximum kınetic energy of oscillation k. emax =5 pdx(y)max = If the value of (y)max at a point x on the string is given by G)max = (A + B3 ) sın? Onx (a) Show that the sum of the energies of the oscillators along the string, that is, the integral gives the expected result (b) What is the implication of the result on the conversation of energy? (Note. the normal frequency wn = NITC/l.) ll 12:33 PM 2021-09-20 Page: 1 of 1 B I E E E 90% e Words: 0 +
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Given,En=mωn2(An2+Bn2)4k.emax=12ρdx(yn2)max=12ρdxωn2(yn2)max(yn2)max=(An2+Bn2)sin2ωnxc

 

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