Toronto Math Forum

APM346-2016F => APM346--Lectures => Chapter 4 => Topic started by: Shaghayegh A on November 14, 2016, 01:55:31 PM

Title: HA6, problem 5 (problems to 4.1 and 4.2)
Post by: Shaghayegh A on November 14, 2016, 01:55:31 PM

Problem 5 of the problems in 4.1 and 4.2 asks to "Consiser oscillations of the beam with the clamped left and the free right end. The boundary conditions are then $$u_{to}+Ku_{xxxx}=0, 0<x<l (9)$$and $$u_{xx}(l,t)=u_{xxx}(l,t)=0 (13)$$. After separating variables and pluggin in boundary counditikns, I get
$$-A \sin(\omega L)-B \cos(\omega L)+ C \sinh(\omega L)+D \cosh(\omega L)=0$$ and
$$A\cos(\omega L)+B \sin(\omega L)+C \cosh(\omega L)+ D \sinh(\omega L)=0$$
This is two equations and four unknowns. How can I solve for A, B, C, D?

Title: Re: HA6, problem 5 (problems to 4.1 and 4.2)
Post by: Victor Ivrii on November 15, 2016, 06:57:55 AM

Quote from: Shaghayegh A on November 14, 2016, 01:55:31 PM

This is two equations and four unknowns. How can I solve for A, B, C, D?

Wrong