Question

An object attached to the end of a spring slides on a horizontal frictionless surface with simple harmonic motion. Assume the maximum displacement of the object is 2 so that it oscillates between +2 and −2. Determine the location(s) at which the object's kinetic energy and potential energy are the same in terms of .

Answer 1

In simple harmonic motion, the energy oscillates between kinetic and potential. In the case of an object attached to a spring sliding on a frictionless surface, the energy is converted from potential to kinetic and vice versa. The velocity becomes zero when the conversion is complete.

Step-by-step explanation:

In simple harmonic motion, the energy oscillates back and forth between kinetic and potential. In the case of an object attached to a spring sliding on a frictionless surface, the motion starts with all the energy stored in the spring. The elastic potential energy is converted to kinetic energy as the object moves, becoming entirely kinetic energy at the equilibrium position. It is then converted back into elastic potential energy by the spring, with the velocity becoming zero when the kinetic energy is completely converted, and so on.