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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)

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1. henpen

Hooke'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

2. germanphysics

Ahh! Thank you!

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