hole through the earth example oscillations gravity

+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