Lecture 7 Notes

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

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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 ....
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## 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.

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