lecture18

# lecture18 - Phys 2101 Gabriela Gonzlez Oscillations =...

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1 Phys 2101 Gabriela González 2 Oscillations = anything that “swings” back and forth. Harmonic oscillations: described with trigonometric functions. Three kinds of oscillations: free, damped and forced. We will focus on free oscillations.

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2 3 4 Displacement: x(t) = x m cos( ω m t + φ ) maximum (peak) amplitude angular frequency phase angle frequency (cps, Hz): f= ω /2 π period (sec) : T=1/f=2 π / ω
3 5 Displacement: x(t) = x m cos( ω t + φ ) Velocity: v(t) = dx(t)/dt = - ω x m sin( ω t + φ ) Acceleration: a(t) = dv(t)/dt = - ω 2 x m cos( ω t + φ ) = - ω 2 x(t) Force: F = m a = ± m ω 2 x = ± k x A spring! ω 2 =k/m A spring force produces oscillations of the mass attached to it. Any oscillation has a “spring-like” (restoring) force. 6 Displacement: x(t) = x m cos( ω t + φ ) Velocity: v(t) = dx(t)/dt = - ω x m sin( ω t + φ ) Acceleration: a(t) = dv(t)/dt = - ω 2 x m cos( ω t + φ )

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4 7 A 5.00 kg block is attached to a spring with spring constant k=2.50 N/cm. If the spring is then stretched 12.0 cm and released from rest, a) what is its period of oscillation? b) what is its maximum amplitude of oscillation? c) what is its maximum speed? d) what is the maximum force the spring will exert on the body? 8
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## This note was uploaded on 12/01/2011 for the course PHYS 2101 taught by Professor Grouptest during the Fall '07 term at LSU.

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lecture18 - Phys 2101 Gabriela Gonzlez Oscillations =...

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