If you increase the weight of an object, the frictional force increases but the coefficient does not change why

The coefficient of friction should in the majority of cases, remain constant no matter what your normal force is. When you apply a greater normal force, the frictional force increases, and your coefficient of friction stays the same. Here's another way to think about it: because the force of friction is equal to the normal force times the coefficient of friction, we expect (in theory) an increase in friction when the normal force is increased.

One more thing, the coefficient of friction is a property of the materials being "rubbed", and this property usually does not depend on the normal force

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

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