Kinetic and Potential Energy!?! This problem is totally confusing me..can someone please explain it... A 3.0 kg object subject to a restoring force F is undergoing simple harmonic motion with a small amplitude. The potential energy U of the object as a function of distance x from its equilibrium is shown. This particular object has a total energy E: of 0.4 J. (a) What is the object's potential energy when its displacement is +4 cm from its equilibrium position? For this problem, I used 4 cm as my displacement, but when I used it in the formula, I ended up getting an answer that is greater than the total energy, so I know it must be wrong. Am I using the wrong displacement? (b) What is the farthest the object moves along the x-axis in the positive direction? Explain. I really don't understand how to solve for the distand in the x-axis without having the acceleration or time. Is there a formula that I've overlooked or am I just making this problem more complicated than it is? (c) Determine the object's kinetic energy when its displacement is -7 cm. For this part, the kinetic energy equation is KE= 1/2mv^2. How do I solve for the velocity without time or acceleration? (d) What is the object's speed at x= 0? Again, I would need the answers from (c) to solve for the speed.
For part 9 (a). Mind your units. The units for Joules is: 1 Joule = 1 kgm^2/s^2. If you are using cm, you will not be getting Joules, but rather "centi-Joules" :P For part (b). The energy of a oscillator can be expressed as the sum of it's potential (1/2kx^2) and kinetic (1/2mv^2). At max displacement, it has zero kinetic energy.
There is a graph of the distance and potential energy. When the problem states that it is 4cm from its equilibrium position, is it referring to the x or y component?