{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture22and23 - F igÙ Öe Ò ØÖÓdÙ c Ø iÓÒ ØÓec...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: F igÙ Öe : Ò ØÖÓdÙ c Ø iÓÒ ØÓec ØÓ ÖF ÙÒ c Ø iÓÒ × :a ÖaÑ e ØÖ iceÔ Öe ×eÒ Øa Ø iÓÒ ×Ó fC Ù ÖÚ e × E a Ö ÐÝ iÒa Øh7Û ed eÒ ed Øh ecÓ × iÒ eaÒd × iÒ e fÙÒ c Ø iÓÒ ×a ×Øh ecÓÓ Öd iÒa Øe×Ó f aÔÓ iÒ ØÑ ÓÚ iÒga ÖÓÙÒd Øh eÙÒ iØc iÖc Ðe ;iÒF igÙ ÖeØh eØh eÔÓ iÒ Ø Ðab e ÐÐed ( x, y ) ha ×cÓÓ Öd iÒa Øe×g iÚ eÒbÝ Øh eeÕÙa Ø iÓÒ × x = cos( ωt ) y = sin( ωt ) t ∈ [0 , 2 π ] Û h eÖe ωt i×Øh eaÒg Ðea ×Ñ ea ×Ù Öed fÖÓÑ Øh eÔÓ × iØ iÚ e x aÜ i×h i×i× iÒ fac Øa × iÑ Ô ÐeeÜaÑ Ô ÐeÓ faÒ eÛÛ aÝÓ fd e×cÖ ib iÒgcÙ ÖÚ e× iÒgeÒ eÖa ÐÒ ×ØeadÓ f×Øa Ø iÒga Öe Ða Ø iÓÒ ×h iÔb e ØÛ eeÒ x aÒd y Û eÑ aÝd e×cÖ ib eeachÓ f x aÒd y a ×a fÙÒ c Ø iÓÒÓ fa Øh iÖdÚa Ö iab Ðe Øh e Ôa ÖaÑ e ØeÖ h eØÛ ÓeÕÙa Ø iÓÒ ×a ÖeÖe feÖÖed ØÓa × Ôa ÖaÑ e ØÖ ic eÕÙa ØiÓÒ × fÓ ÖØh eÙÒ iØc iÖc Ðe fÛ eØh iÒkÓ fØh eÔa ÖaÑ e ØeÖ t a ×ÖeÔ Öe×eÒ Ø iÒg Ø iÑ eØh eÒÛ ecaÒ iÑ ag iÒ e x aÒd y a ×ÖeÔ Öe×eÒ Ø iÒg Øh ecÓÓ Öd iÒa Øe×Ó faÔÓ iÒ ØÛ h ich i×Ñ ÓÚ iÒgabÓÙ Ø iÒ Øh e xy Ô ÐaÒ eaÒd ØÖac iÒgÓÙ ØacÙ ÖÚ ea × iØdÓe××Óh eadÚaÒ ØageÓ fØh i×aÔÔ ÖÓach i×Øha ØÖega Öd Ðe××Ó fÛ h e Øh eÖ y i×a fÙÒ c Ø iÓÒÓ f x Ó Ö x i×a fÙÒ c Ø iÓÒÓ f y Û e caÒa ÐÛ aÝ ×ØÖea Ø x aÒd y a × fÙÒ c Ø iÓÒ ×Ó fØ iÑ eh i×caÒ ×aÚ eÙ × fÖÓÑ haÚ iÒg ØÓb ÖeakÔ ÖÓb ÐeÑ ×dÓÛ Ò iÒ ØÓ×eÔa Öa Øeca ×e× a ×Û eÓ fØeÒhaÚ eØÓdÓ fÓ ÖØh e ÙÒ iØc iÖc ÐeÛ iØh y b e iÒgg iÚ eÒbÝe iØh eÖ √ 1- x 2 Ó Ö- √ 1- x 2 Ó ØehÓÛ eÚ eÖ Øha ØÛ eÚ eac ØÙa ÐÐÝ iÒ ØÖÓdÙ cedÑ Ó Öe iÒ fÓ ÖÑ a Ø iÓÒ ;Û h iÐea Öe Ða Ø iÓÒ ×h iÔb e ØÛ eeÒ x aÒd y d e×cÖ ib e×acÙ ÖÚ eÓÙ ÖÔa ÖaÑ e ØÖ iceÕÙa Ø iÓÒ ×a Ð×Ó iÒd ica ØeØh ed iÖec Ø iÓÒ iÒÛ h ich Øh ecÙ ÖÚ e i×ØÓb eØÖacedÓÙ Øa ×Û e ÐÐa ×Øh e×Ô eedA Ð×ÓbÝÔ Ðac iÒga Öe×ØÖ ic Ø iÓÒÓÒ Øh eÚa ÐÙ e×Ó f t ØÓb ecÓÒ × id eÖedÛ ecaÒ i×Ó Ða Øe×Ô ec ic×ec Ø iÓÒ ×Ó f Øh e×ecÙ ÖÚ e×F Ó ÖØh i×Öea ×ÓÒÛ eÑ ak ead i×Ø iÒ c Ø iÓÒb e ØÛ eeÒ Øh e cÙ ÖÚe aÒd Øh e Ôa Øh F Ó ÖeÜaÑ Ô Ðe fÓ ÖØh eÔa ÖaÑ e ØÖ iceÕÙa Ø iÓÒ ×abÓÚ e E ÕÙa Ø iÓÒ Øh eÔa Øh i× Øh eeÒ Ø iÖeÙÒ iØc iÖc ÐeØÖaÚ eÖ×ed cÓÙÒ ØeÖc ÐÓckÛ i×e×Øa ÖØ iÒg fÖÓÑ Øh eÔÓ iÒ Ø Û iØhaÒgÙ Ða Ö fÖeÕÙ eÒ cÝ ω. ecÓÙ Ðdd e×cÖ ib eeÜac Ø ÐÝ Øh e×aÑ ec iÖc ÐebÝÙ × iÒg Øh eÔa ÖaÑ e ØÖ iceÕÙa Ø iÓÒ × x ( t ) = sin t y ( t ) = cos t t ∈ (0 , 3 π ) ....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern