Final answer:
If the mass in a simple harmonic oscillator is halved, the maximum kinetic energy is also halved, provided that amplitude and velocity remain constant.
Step-by-step explanation:
When a simple harmonic oscillator, consisting of a mass connected to a spring undergoes undamped motion, the system's energy oscillates between kinetic and potential. Specifically, the maximum kinetic energy of an oscillator in SHM is given by the formula K = 1/2mv², where m is the mass and v is the velocity at equilibrium position, where the potential energy is zero and kinetic energy is at its maximum. If the mass of the oscillator is halved, the maximum kinetic energy would also be halved because kinetic energy is directly proportional to the mass, assuming that amplitude and velocity remain constant.
In a simple harmonic oscillator, the maximum kinetic energy occurs at the equilibrium position when the mass is moving fastest. When the mass is halved, the frequency of the motion remains the same, but the maximum potential energy of the system decreases because the spring constant remains constant. Since the total energy of the system is constant in SHM, the decrease in potential energy results in a decrease in maximum kinetic energy. Therefore, if the mass is halved, the maximum kinetic energy will also be halved.