Final answer:
The mechanical energy, maximum speed, and maximum acceleration in a mass-spring system undergoing simple harmonic motion can be calculated using the spring constant, mass of the object, and the amplitude of oscillation.
Step-by-step explanation:
The question involves determining the mechanical energy, maximum speed, and maximum acceleration of a mass-spring system undergoing simple harmonic motion (SHM).
For a mass-spring system in SHM, the mechanical energy (E) of the system is given by:
E = (1/2)kA^2
Where k is the spring constant, and A is the amplitude of oscillation. In this case, k = 221 N/m and A = 0.042 m (since 4.20 cm is converted to meters). Plugging in the values, we can calculate the mechanical energy.
The maximum speed (v_max) of the mass can be found using the formula: v_max = ωA
Where ω is the angular frequency of the system given by ω = sqrt(k/m), and A is again the amplitude. The mass m must be in kilograms, so 454 g converts to 0.454 kg.
Finally, the maximum acceleration (a_max) experienced by the mass is at the maximum displacement and it is given by: a_max = ω^2A
Using the same ω calculated for maximum speed, we can find the maximum acceleration.
Thus, we can calculate the required mechanical energy, maximum speed, and maximum acceleration for the given mass-spring system.