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Smity
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Homework Statement
I have a ball of 20 kg describing a damped harmonic movement, ie,
m*∂^2(x)+R*∂x+K*x=0,
with m=mass, R=resistance, K=spring constant.
The initial position is x(0)=1, the initial velocity is v(0)=0.
Knowing that v(1)=0.5, v(2)=0.3, I have to calculate K and R.
2. The attempt at a solution
I know that if R^2 < 4*m*K, the solution with x(0)=1 and v(0)=0 is such that:
∂x(t)=exp(-R/(2*m)*t)*[-(R/(2*m)^2)/(√[K/m-(R/(2*m))^2])-√[K/m-(R/(2*m))^2]]*sin(√[K/m-(R/(2*m))^2]*t), and I solve the sistem of equations, but it has to be a simpler way to do it (and also I don't use the mass of the ball)
Thanks!