7 damped mass spring m k 0 mx x kx 0 2 mr

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the unit circle. i.e. cos2(A)+sin2(A) = 1. Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: • Example: 4 cos(2t) + 3 sin(2t) ￿ ￿ 4 3 =5 cos(2t) + sin(2t) 5 5 = 5(cos(φ) cos(2t) + sin(φ) sin(2t)) = 5 cos(2t − φ) 4 5 3 φ 4 φ = 0.9273 3 cos(A − B ) = cos(A) cos(B ) + sin(A) sin(B ) (cos(A), sin(A)) must lie on the unit circle. i.e. cos2(A)+sin2(A) = 1. Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: y (t) = C1 cos(ω0 t) + C2 sin(ω0 t) Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: y (t) = C1 cos(ω0 t) + C2 sin(ω0 t) ￿ 2 2 C1 + C2 • Step 1 - Factor out A = . Applications - vibrations (3.7) • Converting from sum-of-sin-cos to a single cos expression: y (t) = C1 cos(ω0 t) + C2 sin(ω0 t) ￿ 2 2 C1 + C2 • Step 1 - Factor out A = • Step 2 - Find the angle and φ for which sin(φ) = ￿ . C1 cos(φ) = ￿ 2 2 C1 + C2 C2 2 C1 + 2 C2 ....
View Full Document

This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.

Ask a homework question - tutors are online