Tuesday, 30 October 2007 - 5:12 PM EDT

by the principles of Newton's laws, the energy would remain the same with the amplitude not changing, only the frequency would change; since more mass would have to be moved from -A to A, it would do so slower without the energy changing

Tuesday, 30 October 2007 - 5:18 PM EDT

No i dont think the energy changes or that the energy is dependant on the mass. Think about it. If you pull the spring back from the rest point x meters and let it go, then as it goes back towards the rest point (the point in the middle of it's simple harmonic motion) it will have Ke and Pe, the Ke getting larger and the Pe getting smaller as it gets closer to the midpoint. That total energy is going to be equal to the Pe that it started with x meters from the midpoint. If you say Pe(spring) + Ke = Pe (spring initial) then the masses all drop out right in the beginning, and thus energy is independent of mass.

Tuesday, 30 October 2007 - 9:33 PM EDT

The total energy of the system would not change because it depends only on the spring constant and the amplitude and since the amplitude is remaining the same, the total energy would remain the same.  As for the kinetic and potential energies, I am not so sure.  I have two ideas on this.  One is that the kinetic energy would increase, therefore decreasing the potential energy, since the total energy stays the same.  I would say this because kinetic energy depends on mass and velocity, so if the mass increased, kinetic energy would increase.  However, I also think that they may stay the same looking at it from the potential energy side of things.  I would say this because potential energy depends on the spring constant and the distance the spring is stretched.  Therefore, if the amplitude stays the same, potential energy stays the same and so does kinetic energy since total stays the same.

Tuesday, 30 October 2007 - 10:02 PM EDT

Yes, my identity is revealed, but I had to since I kept getting zeros for my blogs!

We already derived in this class the formula for the total energy of a spring.  A spring generates simple harmonic motion and the equation for total energy was 1/2kA^2.  This equation clearly shows that energy in simple harmonic motion only depends on a constant and the amplitude of the motion.  Mass does not factor into this equation so mass will not affect the potential, kinetic or total energy of the system. 

Tuesday, 30 October 2007 - 10:20 PM EDT

I think that the total energy would stay the same this is because the total energy of a simple harmonic spring motion is depended on the amplitude and the spring constant. I am assuming that the same spring is used with both masses when saying this because the problem doesn’t say other wise so the spring constant will be the same for both and we know that they will have the same amplitude in both. Since the mass of the object has no impact on the total energy of the system that is why I say the total energy will stay the same. I think that both the kinetic energy and the potential energy of the system will stay the same. We know the potential energy will be the same since it has the same spring constant and will ideally be stretched the same distance as before. We also know that the kinetic energy of the system is dependent on the mass and the velocity. Since the mass is being doubled you would initial think that the kinetic energy would increase however, since its mass is doubled it will have more inertia so the velocity will decrease giving you the same kinetic energy in the end. That is why the total, potential and kinetic energy of this system will be the same with these masses.

Tuesday, 30 October 2007 - 10:44 PM EDT

As has been stated, the total energy of a simple harmonic oscillator is 1/2kA^2 which has nothing to do with the mass, only the spring constant and the amplitude. Therefore that will be unchanged. PE for a spring is 1/2kx^2 which has nothing to do with mass, so that should be unaffected. KE will be unchanged if the total energy will be unchanged, but to compensate the velocity will have to go down. I think.

Tuesday, 30 October 2007 - 11:49 PM EDT

The total energy for a simple harmonic oscilator (spring)  is found through the equation 1/2 kA^2.  So, by looking at this equation you can clearly see that  that if the mass of a block-spring system is doubled and the amplitued stys the same then the total energy will not change since mass is not a factor while solving for the total energy of a spring.  Therefore, it only depends on the constant K and the Amplitude of the simple harmonic oscilator.  For the second part of this problem asking if the PE and KE depend on the mass the answer is no.  This is because the mass again is not a factor of this eqution, consequently meaning that the KE, PE, or Total Energy will not be affected.