Final answer:
The question requires finding the total mechanical energy of a mass-spring system but doesn't provide enough information for a complete solution, as the spring constant is needed to solve for total energy.
Step-by-step explanation:
The question asks to find the total energy of a 6.3 kg object oscillating on a spring with an amplitude of 51.7 cm and a maximum acceleration of 0.9 m/s². In physics, the total mechanical energy (E) of an oscillating spring-mass system is the sum of its potential energy (U, stored in the spring) and kinetic energy (K, due to the object's motion) at any given point. However, at the maximum displacement (amplitude), all the energy is stored as potential energy, and at the maximum acceleration, which occurs at the equilibrium position, all the energy is kinetic energy. The maximum value of either form of energy will equal the total mechanical energy of the system.
To find the total energy, we use the equation for potential energy of a spring (U) at the maximum displacement: U = (1/2)kx². Here k is the spring constant and x is the amplitude. We can also use the equation for the maximum kinetic energy when the object passes through the equilibrium position: K = (1/2)mv², where m is the mass and v is the maximum velocity. Given the maximum acceleration (a), we can derive the maximum velocity using the equation a = - ω²x, where ω is the angular frequency. From the maximum acceleration, we can find ω and then use it to find v. Unfortunately, the necessary information to calculate the total energy as described is not given in the question. Additional information such as the spring constant is needed. Therefore, with the information at hand, we cannot calculate the total energy.