Answer :
Final answer:
In a mass-spring oscillatory system, at maximum amplitude, the mechanical energy is wholly potential energy. This can be represented as E = (1/2) kx². Using the provided mechanical energy and the spring constant, we can calculate the amplitude to be approximately 3.46 cm.
Explanation:
The question is asking you to determine the amplitude of an oscillatory motion in a mass-spring system. The total mechanical energy (E) of the system is given as well as the force constant (k) of the spring and the mass of the object (m).
Firstly, we know that the total mechanical energy of an oscillating system like a mass-spring system is given by E = (1/2) mv² + (1/2) kx², where v is the velocity and x is the displacement which is same as amplitude of oscillation. At the maximum amplitude the velocity of the mass is zero, so the mechanical energy will be totally in the form of potential energy: E = (1/2) kx².
So, we can calculate the amplitude from given mechanical energy and spring constant: x = sqrt((2*E)/k). Substituting given values, x = sqrt((2*0.284)/151), which equals approximately 0.0346 meter or 3.46 cm.
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