Lecture 7 Notes

# 7 converting from sum of sin cos to a single cos

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

This is the end of the preview. Sign up to access the rest of the document.

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 ) +...
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