1. An engineer working at an industrial spring company designs a spring that obeys a force law F (x) = -c(x – Xeq)³ where c is a positive constant and Xeq is the equilibrium position of the spring. a. What are the units of the constant c? Explain. b. Let the equilibrium position xeg = 0 and derive an expression for the system's potential energy as a function of position. c. Make a graph of the force F(x) function and the potential energy U(x) function. d. Explain what an equilibrium position is and how you can find them from a graph of potential energy versus position. Determine if there are any equilibrium positions using your potential energy function. For each position determined, are they stable or unstable? e. Suppose you know the total energy of a system. What other information can be obtained from analyzing a potential energy graph? Explain.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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