Amass is attached to a vertical spring. the mass exhibits simple harmonic motion between points a and b. which of the following statements are true? check all that apply. the mass is located midway between points a and b when its potential energy is at maximum. the mass is located at either point a or b when its kinetic energy is at minimum. the mass is located midway between points a and b when its kinetic energy is at maximum. the mass is located at either point a or b when its potential energy is at minimum.

The mass is located midway between points A and B when its kinetic energy is at maximum.

The mass is located at either point A or B when its potential energy is at minimum.

Explanation:

The mass is moving by simple harmonic motion. A and B represent the points of maximum displacement of the spring-mass system. The total mechanical energy of the system is sum of elastic potential energy (U) and kinetic energy (K):

where

k is the spring constant

x is the displacement (with respect to the equilibrium position)

m is the mass

v is the speed

Due to the conservation of energy, the total mechanical energy E must be constant. This means that:

- When the displacement (x) is maximum (so, at either A or B), the potential energy is maximum, while the kinetic energy is at minimum

- When the displacement (x) is zero (so, at midway between points A and B), the potential energy is at minimum, while the kinetic energy is at maximum

Therefore, the two correct statements are the last two:

- The mass is located midway between points A and B when its kinetic energy is at maximum.

- The mass is located at either point A or B when its potential energy is at minimum.

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