A displacement obeys .

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Ordinary differential equations

Conditions of Validity, Ch The spectral theorem, degeneracy and the matrices that will not diagonalise

Problem

A displacement

y(t)

obeys

\ddot y + 5\dot y + 6y = 0

. ((a)) Write this as

\dot{\mathbf{x}}=\mathsf{A}\mathbf{x}

with

\mathbf{x}=(y,\dot y)

, and show that the eigenvalues of

\mathsf{A}

are the roots of the auxiliary equation. ((b)) Find the eigenvectors of

\mathsf{A}

and use them to write

y(t)

for release from

y(0)=1\,\mathrm{cm}

at rest,

\dot y(0)=0

. Evaluate

y(0.5\,\mathrm{s})

Related theory

Ordinary differential equations

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