Thanks for providing this.
Here is the complete answer to (c, d)
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I correct some typos. Please check this file.
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I have worked out a general solution that you can refer to once you know what E actually represents. I may go to bed very soon and cannot respond to your update in a few hours. But I will check on it once you have obtained more information.
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If E is the total energy (i.e., kinetic + potential), what is the reference point for the potential energy? Potential energy doesn’t have an absolute value, and its value can change if the zero-energy reference point is changed.
Also, if it is the total energy, another degree of freedom come out: I cannot determine the initial state of the system. For instance, I may have the mass at a high altitude with potential energy E, but the object stays still and has no kinetic energy, so the total energy is E. I can also have the mass at a low altitude with potential energy zero, but I give it an initial velocity which grants it kinetic energy E. This will also give me an total energy E. Or maybe I can choose something in between.
I strongly recommend you contact your instructor (or whatever being the source of this problem) for a clarification. I am not able to solve (c, d) with currently insufficient information.
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Need further clarification on (c, d)
Also, are you considering a 2d problem (a simple pendulum), or a more complicated 3d problem (like a Foucault pendulum)?
