The Calculus for Engineers
The Calculus for Engineers
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In our eReader you can find the full English version of the book. Read The Calculus for Engineers Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Calculus for Engineers
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To quickly assess the difficulty of the text, read a short excerpt:
142. Imagine the body to be retarded by a force which dw is proportional to its velocity, or b -j. . Observe that this acts as J acts, that is upwards, towards the position of equi- librium.
Hence we may write Wd^x, dx X Jdt^-^^dt^h^^ (^>- We shall presently see what law now connects x and t in this damped vibration.
143. Suppose that in the last exercise, when the body is displaced x feet downwards, its point of support B is also y feet below its old position. The spring is really only elongat...ed by the amount x—y, and the restoring force is —y-^ • Con- sequently (1) ought to be Wd'x dx x_y J dt^^^Jt^jri ^'^^• Now imagine that the motion y is given as a function of the time, and we are asked to find ix; as a function of the time. Y gives rise to what we call a forced vibration. If 2/ = we have the natural vibrations only.
We give this, not for the purpose of solving it just now, although it is not difficult, but for the purpose of familiar- izing the student with differential equations and inducing him to translate them into ordinary language.
What to read after The Calculus for Engineers?
You can find similar books in the "Read Also" column, or choose other free books by John Perry to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
142. Imagine the body to be retarded by a force which dw is proportional to its velocity, or b -j. . Observe that this acts as J acts, that is upwards, towards the position of equi- librium.
Hence we may write Wd^x, dx X Jdt^-^^dt^h^^ (^>- We shall presently see what law now connects x and t in this damped vibration.
143. Suppose that in the last exercise, when the body is displaced x feet downwards, its point of support B is also y feet below its old position. The spring is really only elongat...ed by the amount x—y, and the restoring force is —y-^ • Con- sequently (1) ought to be Wd'x dx x_y J dt^^^Jt^jri ^'^^• Now imagine that the motion y is given as a function of the time, and we are asked to find ix; as a function of the time. Y gives rise to what we call a forced vibration. If 2/ = we have the natural vibrations only.
We give this, not for the purpose of solving it just now, although it is not difficult, but for the purpose of familiar- izing the student with differential equations and inducing him to translate them into ordinary language.
What to read after The Calculus for Engineers?
You can find similar books in the "Read Also" column, or choose other free books by John Perry to read onlineMoreLess
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