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# capa13 - CAPA set 13 1 Harmonic oscillation The position of...

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CAPA set 13 1) Harmonic oscillation: The position of the tip of the board can be described with an equation of the form: x(t) = A cos( ω t + φ ), with ω = 2 π f = 2 π /T From ‘motion in 1 dimension’ we know that the velocity of the tip of the board can then be described as: dx(t)/dt (‘first derivative of x over t’) For the acceleration we can write: a(t) = dv/dt = d 2 x/dt 2 = -A ω 2 cos( ω t + φ ). Therefore, the maximum acceleration is A ω 2 , ‘A’ being the amplitude of the oscillation. The requirement that the stone does not loose contact w = ith the board means, that the maximum acceleration of the tip of the board is smaller than ‘g’. We therefore can write: A ω 2 =g barb2right A = g/ ω 2 2) Simple harmonic oscillation: When the mass is released it drops, say, by the height ‘2A’. Since it is a mass on a spring it will oscillate back-and-force between the lowest position at x = -A and the highest position at x = A. At the position x=0 the mass will have zero net-force (remember: simple harmonic oscillator: F = -k x). At this position we can

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