Chapter 9.1, Problem 2E

Interpretation Introduction

Interpretation:

To analyse the behaviour of the higher modes of the waterwheel equation.

• (a) To show that for $\text{n }\ne 1$, all modes ${\text{a}}_{\text{n}}{\text{, b}}_{\text{n}}\to 0\text{ as}\text{t}\to \infty \text{ if}\text{Q(θ) =q1 cosθ}\text{.}$

• (b) To analyse the case where $\text{Q(θ) = }{\displaystyle \sum _{n=0}^{\infty }{\text{q}}_{\text{n}}\text{cos(nθ)}}$.

Concept Introduction:

• ➢ The fixed point of a differential equation is the point where $\text{f(x*) = 0 ; while substitution f(x*) = }\dot{\text{x}}\text{ is used and x\&*\#x00A0;is a fixed point}$.

• ➢ The values for which parameters of a differential equation have a non-zero solution under given conditions are called Eigen values.