digraph physicsDerivation { 
overlap = false;
label="derivation: equation of motion for a spring
https://allofphysiscs.com";
fontsize=12;
0004514656 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0004514656 -> generated_expression_5345738321_ca68a59c36c3f075c4a459a042ca7d8f639b88fa6d1d6664748f582f121a86cc;
generated_expression_5345738321_ca68a59c36c3f075c4a459a042ca7d8f639b88fa6d1d6664748f582f121a86cc [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5345738321_ca68a59c36c3f075c4a459a042ca7d8f639b88fa6d1d6664748f582f121a86cc.png",labelloc=b];
0004790069 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0004790069 -> generated_expression_4428528271_f078620b376a825fd7e4affc08b570da06f79345e34597f1d894b71bd0c20f39;
generated_expression_4428528271_f078620b376a825fd7e4affc08b570da06f79345e34597f1d894b71bd0c20f39 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4428528271_f078620b376a825fd7e4affc08b570da06f79345e34597f1d894b71bd0c20f39.png",labelloc=b];
0001216158 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0001216158 -> generated_expression_6831694380_ba0ffcb084f06af67d8427ff1b9fd15d5e18acef4448c7da60b3879ee922ceb6;
generated_expression_6831694380_ba0ffcb084f06af67d8427ff1b9fd15d5e18acef4448c7da60b3879ee922ceb6 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6831694380_ba0ffcb084f06af67d8427ff1b9fd15d5e18acef4448c7da60b3879ee922ceb6.png",labelloc=b];
0005376872 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_LHSofexpr1equalsLHSofexpr2.png",labelloc=b];
generated_expression_4428528271_f078620b376a825fd7e4affc08b570da06f79345e34597f1d894b71bd0c20f39 -> 0005376872;
generated_expression_4428528271_f078620b376a825fd7e4affc08b570da06f79345e34597f1d894b71bd0c20f39 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4428528271_f078620b376a825fd7e4affc08b570da06f79345e34597f1d894b71bd0c20f39.png",labelloc=b];
generated_expression_5345738321_ca68a59c36c3f075c4a459a042ca7d8f639b88fa6d1d6664748f582f121a86cc -> 0005376872;
generated_expression_5345738321_ca68a59c36c3f075c4a459a042ca7d8f639b88fa6d1d6664748f582f121a86cc [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5345738321_ca68a59c36c3f075c4a459a042ca7d8f639b88fa6d1d6664748f582f121a86cc.png",labelloc=b];
0005376872 -> generated_expression_2334518266_237302d3dee171c08dddf2f2d71c518da158773ef879ca060566dca213c67577;
generated_expression_2334518266_237302d3dee171c08dddf2f2d71c518da158773ef879ca060566dca213c67577 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2334518266_237302d3dee171c08dddf2f2d71c518da158773ef879ca060566dca213c67577.png",labelloc=b];
0006129880 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_dividebothsidesby.png",labelloc=b];
generated_expression_2334518266_237302d3dee171c08dddf2f2d71c518da158773ef879ca060566dca213c67577 -> 0006129880;
generated_expression_2334518266_237302d3dee171c08dddf2f2d71c518da158773ef879ca060566dca213c67577 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2334518266_237302d3dee171c08dddf2f2d71c518da158773ef879ca060566dca213c67577.png",labelloc=b];
0006129880 -> generated_expression_8655294002_94fa6f8a7343a44138570f48e80c57ad925828f0933c1557c18bbd7599ec3ebb;
generated_expression_8655294002_94fa6f8a7343a44138570f48e80c57ad925828f0933c1557c18bbd7599ec3ebb [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8655294002_94fa6f8a7343a44138570f48e80c57ad925828f0933c1557c18bbd7599ec3ebb.png",labelloc=b];
generated_feed_3634715785_62c66a7a5dd70c3146618063c344e531e6d4b59e379808443ce962b3abd63c5a -> 0006129880;
generated_feed_3634715785_62c66a7a5dd70c3146618063c344e531e6d4b59e379808443ce962b3abd63c5a [shape=box, color=red,label="",image="/code/static/generated_feed_3634715785_62c66a7a5dd70c3146618063c344e531e6d4b59e379808443ce962b3abd63c5a.png",labelloc=b];
0005272817 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_LHSofexpr1equalsLHSofexpr2.png",labelloc=b];
generated_expression_6831694380_ba0ffcb084f06af67d8427ff1b9fd15d5e18acef4448c7da60b3879ee922ceb6 -> 0005272817;
generated_expression_6831694380_ba0ffcb084f06af67d8427ff1b9fd15d5e18acef4448c7da60b3879ee922ceb6 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6831694380_ba0ffcb084f06af67d8427ff1b9fd15d5e18acef4448c7da60b3879ee922ceb6.png",labelloc=b];
generated_expression_8655294002_94fa6f8a7343a44138570f48e80c57ad925828f0933c1557c18bbd7599ec3ebb -> 0005272817;
generated_expression_8655294002_94fa6f8a7343a44138570f48e80c57ad925828f0933c1557c18bbd7599ec3ebb [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8655294002_94fa6f8a7343a44138570f48e80c57ad925828f0933c1557c18bbd7599ec3ebb.png",labelloc=b];
0005272817 -> generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f;
generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f.png",labelloc=b];
0002315272 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareguesssolution.png",labelloc=b];
generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f -> 0002315272;
generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f.png",labelloc=b];
0002315272 -> generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91;
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91.png",labelloc=b];
0008476862 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_differentiatewithrespectto.png",labelloc=b];
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 -> 0008476862;
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91.png",labelloc=b];
0008476862 -> generated_expression_7652131521_943cfb8617153410727140a2845f786c90edbe8849dd40e3e48c6f62aeff2622;
generated_expression_7652131521_943cfb8617153410727140a2845f786c90edbe8849dd40e3e48c6f62aeff2622 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7652131521_943cfb8617153410727140a2845f786c90edbe8849dd40e3e48c6f62aeff2622.png",labelloc=b];
generated_feed_5846177002_e3b98a4da31a127d4bde6e43033f66ba274cab0eb7eb1c70ec41402bf6273dd8 -> 0008476862;
generated_feed_5846177002_e3b98a4da31a127d4bde6e43033f66ba274cab0eb7eb1c70ec41402bf6273dd8 [shape=box, color=red,label="",image="/code/static/generated_feed_5846177002_e3b98a4da31a127d4bde6e43033f66ba274cab0eb7eb1c70ec41402bf6273dd8.png",labelloc=b];
0005435505 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_differentiatewithrespectto.png",labelloc=b];
generated_expression_7652131521_943cfb8617153410727140a2845f786c90edbe8849dd40e3e48c6f62aeff2622 -> 0005435505;
generated_expression_7652131521_943cfb8617153410727140a2845f786c90edbe8849dd40e3e48c6f62aeff2622 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7652131521_943cfb8617153410727140a2845f786c90edbe8849dd40e3e48c6f62aeff2622.png",labelloc=b];
0005435505 -> generated_expression_5945893986_d1c72300950f23bdfae630eaed8c52528a10b20c4ce573cd3f89487a049a178c;
generated_expression_5945893986_d1c72300950f23bdfae630eaed8c52528a10b20c4ce573cd3f89487a049a178c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5945893986_d1c72300950f23bdfae630eaed8c52528a10b20c4ce573cd3f89487a049a178c.png",labelloc=b];
generated_feed_1451839362_e3b98a4da31a127d4bde6e43033f66ba274cab0eb7eb1c70ec41402bf6273dd8 -> 0005435505;
generated_feed_1451839362_e3b98a4da31a127d4bde6e43033f66ba274cab0eb7eb1c70ec41402bf6273dd8 [shape=box, color=red,label="",image="/code/static/generated_feed_1451839362_e3b98a4da31a127d4bde6e43033f66ba274cab0eb7eb1c70ec41402bf6273dd8.png",labelloc=b];
0003234596 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_LHSofexpr1equalsLHSofexpr2.png",labelloc=b];
generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f -> 0003234596;
generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8991236357_574d1901611d2425c90b99c70a4a52130a64e0aa1a6740e6bfa5bae736b9599f.png",labelloc=b];
generated_expression_5945893986_d1c72300950f23bdfae630eaed8c52528a10b20c4ce573cd3f89487a049a178c -> 0003234596;
generated_expression_5945893986_d1c72300950f23bdfae630eaed8c52528a10b20c4ce573cd3f89487a049a178c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5945893986_d1c72300950f23bdfae630eaed8c52528a10b20c4ce573cd3f89487a049a178c.png",labelloc=b];
0003234596 -> generated_expression_1772973171_a2c3369e82f31d95268aff3b45dc9d75ede8ca4fa1592d4631489ef8650a37db;
generated_expression_1772973171_a2c3369e82f31d95268aff3b45dc9d75ede8ca4fa1592d4631489ef8650a37db [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1772973171_a2c3369e82f31d95268aff3b45dc9d75ede8ca4fa1592d4631489ef8650a37db.png",labelloc=b];
0004208810 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_1772973171_a2c3369e82f31d95268aff3b45dc9d75ede8ca4fa1592d4631489ef8650a37db -> 0004208810;
generated_expression_1772973171_a2c3369e82f31d95268aff3b45dc9d75ede8ca4fa1592d4631489ef8650a37db [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1772973171_a2c3369e82f31d95268aff3b45dc9d75ede8ca4fa1592d4631489ef8650a37db.png",labelloc=b];
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 -> 0004208810;
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91.png",labelloc=b];
0004208810 -> generated_expression_2148049269_c793566bd0672d04b74ebac1ad720ec80d1b3ca151661417b64b10d574a6816e;
generated_expression_2148049269_c793566bd0672d04b74ebac1ad720ec80d1b3ca151661417b64b10d574a6816e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2148049269_c793566bd0672d04b74ebac1ad720ec80d1b3ca151661417b64b10d574a6816e.png",labelloc=b];
0005391046 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_multiplybothsidesby.png",labelloc=b];
generated_expression_2148049269_c793566bd0672d04b74ebac1ad720ec80d1b3ca151661417b64b10d574a6816e -> 0005391046;
generated_expression_2148049269_c793566bd0672d04b74ebac1ad720ec80d1b3ca151661417b64b10d574a6816e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2148049269_c793566bd0672d04b74ebac1ad720ec80d1b3ca151661417b64b10d574a6816e.png",labelloc=b];
0005391046 -> generated_expression_1931103031_4984cbc3e45d5dd62415d87345ad394861acfee0a1543ae7828b73c2387dbf74;
generated_expression_1931103031_4984cbc3e45d5dd62415d87345ad394861acfee0a1543ae7828b73c2387dbf74 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1931103031_4984cbc3e45d5dd62415d87345ad394861acfee0a1543ae7828b73c2387dbf74.png",labelloc=b];
generated_feed_7473576008_e854f5f0be37574195ea06266a9eecf31be69a6af402b40b670d79dd318d336c -> 0005391046;
generated_feed_7473576008_e854f5f0be37574195ea06266a9eecf31be69a6af402b40b670d79dd318d336c [shape=box, color=red,label="",image="/code/static/generated_feed_7473576008_e854f5f0be37574195ea06266a9eecf31be69a6af402b40b670d79dd318d336c.png",labelloc=b];
0004482244 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_squarerootbothsides.png",labelloc=b];
generated_expression_1931103031_4984cbc3e45d5dd62415d87345ad394861acfee0a1543ae7828b73c2387dbf74 -> 0004482244;
generated_expression_1931103031_4984cbc3e45d5dd62415d87345ad394861acfee0a1543ae7828b73c2387dbf74 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1931103031_4984cbc3e45d5dd62415d87345ad394861acfee0a1543ae7828b73c2387dbf74.png",labelloc=b];
0004482244 -> generated_expression_1888494137_6cb6319386560cba86bcc31b125d214739d946141d3fac20c9d4ffe594bc4d71;
generated_expression_1888494137_6cb6319386560cba86bcc31b125d214739d946141d3fac20c9d4ffe594bc4d71 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1888494137_6cb6319386560cba86bcc31b125d214739d946141d3fac20c9d4ffe594bc4d71.png",labelloc=b];
0004482244 -> generated_expression_1784114349_8a4867492a1b0b778e3a6d570232800c76fd453c979cc6ee08e06156fbd293fc;
generated_expression_1784114349_8a4867492a1b0b778e3a6d570232800c76fd453c979cc6ee08e06156fbd293fc [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1784114349_8a4867492a1b0b778e3a6d570232800c76fd453c979cc6ee08e06156fbd293fc.png",labelloc=b];
0008522636 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteRHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 -> 0008522636;
generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5415824175_35003f1d34439fca31a6b0da47ab2df1578d2448535801063f0ecfc2c404cd91.png",labelloc=b];
generated_expression_1784114349_8a4867492a1b0b778e3a6d570232800c76fd453c979cc6ee08e06156fbd293fc -> 0008522636;
generated_expression_1784114349_8a4867492a1b0b778e3a6d570232800c76fd453c979cc6ee08e06156fbd293fc [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1784114349_8a4867492a1b0b778e3a6d570232800c76fd453c979cc6ee08e06156fbd293fc.png",labelloc=b];
0008522636 -> generated_expression_6908055431_abb0e2f02ca1ea2c9a0e3c6ea2636a65cdc6402d46340ab38ac2f50f472f3c21;
generated_expression_6908055431_abb0e2f02ca1ea2c9a0e3c6ea2636a65cdc6402d46340ab38ac2f50f472f3c21 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6908055431_abb0e2f02ca1ea2c9a0e3c6ea2636a65cdc6402d46340ab38ac2f50f472f3c21.png",labelloc=b];
0008719992 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declarefinalexpression.png",labelloc=b];
generated_expression_6908055431_abb0e2f02ca1ea2c9a0e3c6ea2636a65cdc6402d46340ab38ac2f50f472f3c21 -> 0008719992;
generated_expression_6908055431_abb0e2f02ca1ea2c9a0e3c6ea2636a65cdc6402d46340ab38ac2f50f472f3c21 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6908055431_abb0e2f02ca1ea2c9a0e3c6ea2636a65cdc6402d46340ab38ac2f50f472f3c21.png",labelloc=b];
}