I need help with part C, I only have one more attempt. Problem 19.26 A spring wi

Question

I need help with part C, I only have one more attempt.

Problem 19.26 A spring with a spring constant of 1200 N/m has a 55-g ball at its end. The energy of the system is 9.0 J . Part A What is the amplitude A of vibration? Express your answer to two significant figures and include the appropriate units. A = 0.12 m Submit My Answers Give Up Correct Part B What is the maximum speed of the ball? Express your answer to two significant figures and include the appropriate units. umaz 18 Submit My Answers Give Up Correct Part C What is the speed when the ball is at a position z = +A/2. Express your answer to two significant figures and include the appropriate units. 2

Explanation / Answer

given spring with spring constant 1200 N/m
mass m = 0.055 kg
Energy, E = 9 J

so the equation of motion can be x = Asin(wt)
w = sqroot(k/m)
v = x' = Awcos(wt) = Aw*sqroot(1 - sin^2(wt)) = Awsqroot( 1 - x^2/A^2) = w*sqroot(A^2 - x^2)
so, for A = 0.12 m
w = sqroot(k/m) = sqroot(1200/0.055) = 147.7

v when x = A/2 = w*sqroot(A^2 - A^2/4) = w*A*sqroot(3)/2
v = 147.7*0.12*sqroot(3)/2 = 15.35 m/s

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