![]() So the A cancels out, giving k = -4Mπ^2/T^2. And k = Force divide by displacement, giving k = maximum force divide by the simultaneous maximum displacement, which gives k = (-A4Mπ^2/T^2)/A.Ħ. So we can get maximum acceleration = -A4π^2/T^2. Since we know the amplitude, and we also know the maximum displacement is at t = T/4, which is at Bt = π/2, which is when sin(Bt) = 1, simultaneously having the greatest acceleration of this oscillating system.ĥ. Deriving once will give (A2π/T)sin(2πt/T), which is the function of velocity.ģ. Giving the Asin(Bt) equation as (Amplitude)sin(2πt/T)Ģ. ![]() I actually derived the formula of k = 4π^2m/T^2 by differentiating the sin(t) function of displacement twice to find the acceleration, then multiply by mass and divide by amplitude to find spring constant.įirst by finding the specific sin(t) function in the form of Asin(Bt), through the given amplitude(A) and period(T).ġ. ![]()
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