7 converting from sum of sin cos to a single cos

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Unformatted text preview: ons - vibrations (3.7) • Undamped mass spring mx + kx = 0 ￿￿ mr +￿ = 0 k k r=± i m 2 x(t) = C1 cos(ω0 t) + C2 sin(ω0 t) Applications - vibrations (3.7) • Undamped mass spring mx + kx = 0 ￿￿ mr +￿ = 0 k k r=± i m 2 x(t) = C1 cos(ω0 t) + C2 sin(ω0 t) ￿ k ω0 = m Applications - vibrations (3.7) • Undamped mass spring mx + kx = 0 ￿￿ mr +￿ = 0 k k r=± i m 2 x(t) = C1 cos(ω0 t) + C2 sin(ω0 t) ￿ k • frequency ω0 = m • increases with stiffness • decreases with mass Applications - vibrations (3.7) Trig identity reminders sin(A + B ) = sin(A) cos(B ) + cos(A) sin(B ) cos(A + B ) = cos(A) cos(B ) − sin(A) sin(B ) Applications - vibrations (3.7) Trig identity reminders sin(A + B ) = sin(A) cos(B ) + cos(A) sin(B ) cos(A + B ) = cos(A) cos(B ) − sin(A) sin(B ) 2 cos(3t + π /3) = (A) 2 sin(π /3) cos(3t) − 2 sin(π /3) cos(3t) (B) 2 sin(π /3) cos(3t) + 2 sin(π /3) cos(3t) (C) 2 cos(π /3) cos(3t) − 2 sin(π /3) sin(3t) (D) 2 cos(π /3) cos(3t) + 2 sin(π /3) sin(3t) (E) Don’t know / still thinking. Applications - vibrations (3.7) Trig identity reminders sin(A + B ) = sin(A) cos(B ) +...
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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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