A 1.90-kg object is attached to a spring and placed on frictionless, horizontal

Question

A 1.90-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 5.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations. Find the force constant of the spring. N/m Find the frequency of the oscillations. Hz Find the maximum speed of the object. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s Where does this maximum speed occur? x = plusminus Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m Find the maximum acceleration of the object. m/s2 Where does the maximum acceleration occur? x = plusminus m Find the total energy of the oscillating system. 0.5 J Find the speed of the object when its position is equal to one-third of the maximum value. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s Find the acceleration of the object when its position is equal to one-third of the maximum value. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s2

Explanation / Answer

c) 1/2 mv^2 = 1/2 k A^2 1.9*v^2 = 25*.2^2 v=0.725 m/s d) x=0 e) use ma = kA a = kA/m = 25*.2/1.9=2.63 f) at .2 h) 1/2 kx^2 + 1/2 mv^2 = 1/2 kA^2 25*(.2/3)^2 + 1.9*v^2 = 25*.2^2 v=.684 m/s i) a = k x/m = max a/3 = 2.63/3=0.877

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