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###### For mass m attached to spring with spring constant k, Newton's Second Law says the displacement of the mass, x (t), should obey the differential equation d2x k = x(t) dt2 m If the mass crosses x = 0 at time t = 0, then one can show the displacement should be given by function of the form c(t) = A cos(bt) where A and b are constants and b is positive_(a) Compute the second derivative of x (t) = Acos (bt) using x (t) Acos (bt) . Do not include x (t) in your answer. d2(b) If the given differen

For mass m attached to spring with spring constant k, Newton's Second Law says the displacement of the mass, x (t), should obey the differential equation d2x k = x(t) dt2 m If the mass crosses x = 0 at time t = 0, then one can show the displacement should be given by function of the form c(t) = A cos(bt) where A and b are constants and b is positive_ (a) Compute the second derivative of x (t) = Acos (bt) using x (t) Acos (bt) . Do not include x (t) in your answer. d2 (b) If the given differential equation holds, then how does the constant b relate to the spring constant k and the mass m? b =

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