{"id":724,"date":"2010-11-15T04:00:00","date_gmt":"2010-11-15T08:00:00","guid":{"rendered":"http:\/\/johncohn.org\/base\/2010\/11\/16\/monday-night-questions\/"},"modified":"2010-11-29T01:34:12","modified_gmt":"2010-11-29T05:34:12","slug":"monday-night-questions","status":"publish","type":"post","link":"http:\/\/johncohn.org\/base\/2010\/11\/15\/monday-night-questions\/","title":{"rendered":"Monday night – questions ?"},"content":{"rendered":"
\n

\t\t\t\t\t\t One of the weird\/fun\u00a0 things about having been a visible face of science on TV is that I sometimes get science and math questions from people I never met.. some are simple .. others are pretty sophisticated..\u00a0\u00a0 some are jsut plain wierd..<\/p>\n

Last night I got a note from a guy I; ve never met who needed help choosing between two laptops..\u00a0\u00a0 Ha !<\/p>\n

My favorite came today.. I was busy ‘working’ during a conference call.. when the following window popped up in facebook .. It was from a guy named Charlie in Sydney Australia. whom I’ve never met.\u00a0 He has a differential equations test tomorrow.. and he needed help on a problem They were studying the Laplace transform .. and all is friends were already asleep.. <\/p>\n

<\/a><\/p>\n

Here’s the problem.. <\/p>\n

<\/a> <\/p>\n

\u00a0My friend wayne and I stared at it a it. got out the Laplace tables and came up with an answer .. (i think..)<\/p>\n

I transformed <\/p>\n

y” + 16y = f(t)
into<\/p>\n

s^2y(s) – sy'(0) + y(0) + 16 y(s) = 0<\/p>\n

which simplified to (when using boundry conditions of y'(0) =0 and y(0) = 1 , for the case t> pi<\/p>\n

y(s) (s2+16) = 1<\/p>\n

so<\/p>\n

y(s) = 1\/(s^2+16)<\/p>\n

which un-transforms (i think) to <\/p>\n

1\/4 sin(4t)<\/p>\n

for the case 0< t < pi, I inverse transformed cos(4t) <\/p>\n

i got s^2y(s) -1 + 16y(s) = 1\/(s^2 + 16) <\/p>\n

which I think simplifies to 4sin(4t) (t\/2+1)<\/p>\n

i think we need to add constants to make the boundary conditions work out.. <\/p>\n

so maybe <\/p>\n

1\/4 sin(4t) + 1 : t> pi
4sin(4t) (t\/2+1) +1 : 0 < t < pi<\/p>\n

But that doesn’t\u00a0 look right..
What did\u00a0 I do wrong ? <\/p>\n

I’ll go sleep on it<\/p>\n

good luck on your test Charlie.. !<\/p>\n

nite all , nite sam
-me<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

One of the weird\/fun\u00a0 things about having been a visible face of science on TV is that I sometimes get science and math questions from people I never met.. some are simple .. others are pretty sophisticated..\u00a0\u00a0 some are jsut plain wierd.. Last night I got a note from a guy I; ve never met … Continue reading Monday night – questions ?<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-724","post","type-post","status-publish","format-standard","hentry"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/posts\/724","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/comments?post=724"}],"version-history":[{"count":1,"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/posts\/724\/revisions"}],"predecessor-version":[{"id":1487,"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/posts\/724\/revisions\/1487"}],"wp:attachment":[{"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/media?parent=724"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/categories?post=724"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/johncohn.org\/base\/wp-json\/wp\/v2\/tags?post=724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}