We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 01 February 2024
This project focuses on the Initial Value Problem (IVP) for ordinary differential equations with the application of multipoint recursion schemes. The effectiveness and convergence of these schemes are explored and subsequently applied to examine the properties of a compound pendulum, specifically the dependence of the oscillation period on energy. The chapter then focuses on Newton’s laws of motion, laying the foundation for understanding the motion equation. The project uses a simple pendulum to illustrate the concept, looking at how changes in amplitude affect the period of harmonic oscillations. Numerical methods, such as recursive methods based on local extrapolation, are then employed to derive formulas. The project concludes by discussing the integration of Runge–Kutta methods and implicit schemes to solve the equations. This project ultimately questions the viability of the pendulum as a standard unit of time, adding value to ongoing discussions in physics and mathematics education.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
