Final answer:
The total mechanical energy of a 2.0 kg mass attached to a spring with a force constant of 10.0 N/m undergoing simple harmonic motion with an initial displacement of 3.0 cm is 0.5 J.
Step-by-step explanation:
The question relates to the total mechanical energy in a system undergoing simple harmonic motion. In such a system, the total mechanical energy (E) is the sum of the potential energy (U) stored in the spring and the kinetic energy (K) of the mass. Since the object starts from its initial displacement and at rest, its initial kinetic energy is zero and all its mechanical energy is potential energy.
The potential energy in a spring is given by the formula U = 1/2 * k * x2, where 'k' is the spring constant and 'x' is the displacement from the equilibrium position. In this case, the spring constant is 10.0 N/m and the displacement is 3.0 cm (which should be converted to meters to match the units of the spring constant). Thus, the potential energy is U = 1/2 * 10.0 N/m * (0.03 m)2.
Performing the calculation:
- U = 1/2 * 10 N/m * 0.0009 m2
- U = 0.005 J
- U = 0.5 J