In case of mechanical wave a particle oscillates and during oscillation its kinetic energy and potential energy changes.
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Solution
A) When a particle passes through the mean position, for eg a block attached to a spring, the extension in the spring is minimum, therefore, the potential energy is minimum and since the particle has the maximum velocity at this position, the kinetic energy will be maximum
Same is the case for C)
B) At the extremes, for eg when a block is attached to a spring that is elongated to a maximum value, all of its kinetic energy is converted to potential energy and therefore, kinetic energy is minimum and the potential energy is maximum.