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germanphysics
 2 years ago
Spring calculation: Acos(wt+phi). How is this derived? And why follows for the deflection: x=(0,100m)*cos (8,08t) ? (D=19,6 N/m; w=8,08s^1 ; T=0,777s and f=1,29 Hz)
germanphysics
 2 years ago
Spring calculation: Acos(wt+phi). How is this derived? And why follows for the deflection: x=(0,100m)*cos (8,08t) ? (D=19,6 N/m; w=8,08s^1 ; T=0,777s and f=1,29 Hz)

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henpen
 2 years ago
Best ResponseYou've already chosen the best response.2Hooke's Law. Force=mass*acceleratio n:\[ma=kx\]\[m\frac{d^2x}{dt^2}+kx=0\]\[\frac{d^2x}{dt^2}+\frac{k}{m}x=0\] \[x=Acos(at+b)\]Is a solution to this (that is, when you put it in the equation, it always spits out 0)(you can actually assume that x is an exponential, and you get an imaginary exponent (i.e. trig functions by Euler's theorem), which you take the real part of to get the same answer). I don't quite understand the second question
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