hole through the earth example oscillations gravity

4
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

Upload: yatn-bangad

Post on 16-Dec-2015

3 views

Category:

Documents


0 download

DESCRIPTION

Simple Harmonic Motion of a body through tunnel in earth

TRANSCRIPT

  • +ROH7KURXJKWKH(DUWK([DPSOH

    KWWSK\SHUSK\VLFVSK\DVWUJVXHGXKEDVHPHFKDQLFVHDUWKROHKWPO

    -RXUQH\WKURXJKWKHFHQWHURIWKH(DUWK

    6XSSRVH\RXFRXOGGULOODKROHWKURXJKWKH(DUWKDQGWKHQGURSLQWRLW+RZORQJZRXOGLWWDNH\RXWRSRSXSRQWKHRWKHUVLGHRIWKH(DUWK"

  • +ROH7KURXJKWKH(DUWK([DPSOH

    KWWSK\SHUSK\VLFVSK\DVWUJVXHGXKEDVHPHFKDQLFVHDUWKROHKWPO

    2QPDVVLQVLGHWKHVKHOO

    7DNLQJSRVLWLYHUDVRXWZDUGIURPWKHFHQWHURIWKH(DUWK

    7KLVLVWKHVDPHIRUPDV+RRNHV/DZIRUDPDVVRQDVSULQJ,WZRXOGFDXVHWKHWUDQV(DUWKWUDYHOHUWRRVFLOODWHEDFNDQGIRUWKWKURXJKWKHFHQWHURIWKH(DUWKOLNHDPDVVEREELQJXSDQGGRZQRQDVSULQJ7KHDQJXODUIUHTXHQF\DQGSHULRGIRUWKLVRVFLOODWLRQDUH

    )RUWKLVFDVHWKHSHULRGRIRVFLOODWLRQLV

    7KHWUDYHOHUDFFHOHUDWHVWRZDUGWKHFHQWHURIWKH(DUWKDQGLVPRPHQWDULO\ZHLJKWOHVVZKHQSDVVLQJWKURXJKWKHJHRPHWULFFHQWHUDWDERXWPVRUDOPRVWPLOHVKU7KHWUDYHOHUZRXOGSRSXSRQWKHRSSRVLWHVLGHRIWKH(DUWKDIWHUDOLWWOHPRUHWKDQPLQXWHV%XWXQOHVVKHRUVKHJUDEVVRPHWKLQJWRKROGRQWKH\ZLOOIDOOEDFNIRUDUHWXUQMRXUQH\DQGFRQWLQXHWRRVFLOODWHZLWKDURXQGWULSWLPHRIPLQXWHV

    $VDIXUWKHUIHDWXUHRIWKLVIDQFLIXOMRXUQH\VXSSRVHDVDWHOOLWHFRXOGEHSXWLQDFLUFXODURUELWDERXWWKH(DUWKULJKWDERYHWKHVXUIDFH,JQRULQJDLUGUDJDQGWKHWHUULILFVRQLFERRPWKDWZRXOGDFFRPSDQ\VXFKDQRUELWVXSSRVHLWSDVVHGRYHUKHDGMXVWDERYHWKHIDOOLQJSHUVRQDVWKH\SRSSHGXSRXWRIWKHKROH7KHSHULRGRIVXFKDQRUELWZRXOGEHVXFKWKDWLWZRXOGEHSDVVLQJRYHUKHDGHYHU\WLPHWKHRVFLOODWLQJSHUVRQSRSSHGXSRQHLWKHUVLGHRIWKH(DUWK

    ,QGH[

    1HZWRQVODZV

    *UDYLW\FRQFHSWV

  • +ROH7KURXJKWKH(DUWK([DPSOH

    KWWSK\SHUSK\VLFVSK\DVWUJVXHGXKEDVHPHFKDQLFVHDUWKROHKWPO

    7KHSHULRGRIWKHRUELWLVFDOFXODWHGIURP

    ZKLFKLVWKHVDPHDVWKHSHULRGRIWKHRVFLOODWLQJERG\

    6DQLW\FKHFNRQWKHKROHWKURXJKWKH(DUWKH[DPSOH

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

    6RWKHKROHWKURXJKWKHFHQWHURIWKH(DUWKUHDOO\GRHVQWZRUNEXWWKLVH[DPSOHKDVJHQHUDWHGVRPHLQWHUHVWLQJFRPPHQWV+DYLQJVZHSWDOOWKHVHGLIILFXOWLHVXQGHUWKHUXJLQSRVWLQJWKLVH[DPSOHLW\HWJLYHVVRPHLQWHUHVWLQJFRUUHODWLRQVWRRUELWDOYHORFLWLHVDQGVXUSULVLQJO\WR+RRNHVODZ

    2WKHUH[DPSOHVRIZHLJKWOHVVQHVV

    +\SHU3K\VLFV

    0HFKDQLFV 51DYH*R%DFN

  • +ROH7KURXJKWKH(DUWK([DPSOH

    KWWSK\SHUSK\VLFVSK\DVWUJVXHGXKEDVHPHFKDQLFVHDUWKROHKWPO