Final answer:
To find the maximum kinetic and potential energies in simple harmonic motion, we use the conservation of energy and equations for kinetic and potential energy at points of maximum displacement and speed. The maximum kinetic energy occurs at the equilibrium point and the maximum potential energy when the object is at its maximum amplitude. At the midway point, energy is shared equally between kinetic and potential forms.
Step-by-step explanation:
The subject of this question is calculating the maximum kinetic energy, maximum potential energy, and the energies at the midway point in simple harmonic motion (SHM). For an object in SHM, the total mechanical energy is conserved, meaning that the sum of kinetic and potential energies remains constant throughout the motion.
The maximum kinetic energy (K) occurs when the object is at the equilibrium position (x = 0) and is given by the formula K = 1/2mv² where m is the mass and v is the maximum velocity. The maximum potential energy (U) is when the object is at its maximum displacement (x = amplitude) and can be calculated using U = 1/2kx² where k is the spring constant and x is the displacement from equilibrium. To calculate these values, we need the spring constant, which is determined by k = mω², where ω is the angular frequency (ω = 2π f).
For an object with a mass of 0.35 kg, amplitude of 140 mm (0.14 m), and a frequency of 0.60 Hz, the spring constant k is calculated as follows: k = mω² = 0.35 kg × (2π × 0.60 Hz)². The maximum velocity v at the equilibrium point can be found by v = ω × amplitude. Using these values and the conservation of energy, the maximum kinetic energy will be equal to the total energy of the system, and the maximum potential energy will be equal when the object is at the amplitude.
At the midway point between the center and the extremity of the motion, the energies will be equally shared between kinetic and potential energy, thus each will be half of the total mechanical energy.