Question

Does amplitude of a spring mass system change when mass is added?

So this is the last question to the AP Physics 1 2018 exam. The surface of the floor is frictionless. Block P was oscillating and then block Q was dropped on top of it. Will the amplitude of of the system stay the same?

Answer 1

See below

Explanation:

More detailed answer to a very similar question here here

Answer 2

If amplitude means max displacement, then no change.

Explanation:

Note: read thru the conservation below. It appears that my understanding of the situation was been faulty.

Amplitude in such a system is generally the magnitude of max displacement from the spring's neutral position. System energy ideally would remain the same as before. The system's energy is exchanged back and forth between kinetic energy and spring potential energy.

When passing the neutral position, all the energy will be kinetic. Since mass is part of the formula for kinetic energy, the velocity must be decreased for the kinetic energy at that location to be the same as before. When at max displacement, mass is not part of the formula for the energy (spring potential energy), so the max displacement should be same as before.

If amplitude means max displacement, then no change.

I hope this helps,
Steve