Home » Hookes Law, the Period of Oscillation and the Kappa-Tau Theorem (The New Mathematics for the Millions Book 2) by Patrick Bruskiewich # Hookes Law, the Period of Oscillation and the Kappa-Tau Theorem (The New Mathematics for the Millions Book 2)

## Patrick Bruskiewich

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29 pages
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 About the Book The Kappa-Tau Theorem, or κ – τ Theorem, is a useful tool to understand the behaviour of many vibrating systems.The Kappa-Tau Theorem is simple to present:If there is a linear relationship between the displacement x in a system pushed out ofMoreThe Kappa-Tau Theorem, or κ – τ Theorem, is a useful tool to understand the behaviour of many vibrating systems.The Kappa-Tau Theorem is simple to present:If there is a linear relationship between the displacement x in a system pushed out of equilibrium, and the force restoring it into equilibrium (Frestoring), such thatFRestoring = – κ xand if we can determine an expression for κ,κ = | Frestoring / x |(we have used the absolute value to avoid confusion due to the sign) then the period τ of simple harmonic oscillation the system is given byτ = 2π √ ( m / κ )Eleven different systems are presented in this volume, from the oscillating spring, to an oscillating magnetic dipole. Keplers Third Law of Planetary Motion is also derived using the kappa-tau theorem.Becoming proficient the Kappa-Tau Theorem and its application to problems in mathematics, physics and engineering is a fine investment of perhaps an hour of your time.Anyone who has mastered middle school algebra and a little high school mathematics can master both this book and the Kappa-Tau Theorem. You don’t even need to know Calculus – this little book with its appendices explains all you need to know to understand its content.In this little book, Volume Two: The New Mathematics for the Millions, The Kappa-Tau theorem is presented from the standpoint of algebra and not geometry.There are several questions included with this book, which are meant to challenge the reader.