KHW 1 CH 15 Spring 2019 Item 4 Learning Goal: To learn to apply the law of conservation of energy to the analysis of harmonic oscillators

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KHW 1 CH 15 Spring 2019 Item 4 Learning Goal: To learn to apply the law of conservation of energy to the analysis of harmonic oscillators. Systems in simple harmonic motion, or harmonic oscillators obey the law of conservation of energy just like all other systems do. Using energy considerations, one can analyze many aspects of motion of the oscillator. Such an analysis can be simplified if one assumes that mechanical energy is not dissipated. In other words, E = K + U-constant, where E is the total mechanical energy of the system, K is the kinetic energy, and U is the potential energy Figure 1 of 1 -A-A 0 A 2 A A MMMMMMMMNANN MMMMANNANNNNAN m nmVNN
a common example of a harmonic oscillator is a mass attached to a spring. In this problem, we will consider a horizontally moving block attached to a spring Note that, since the gravitational potential energy is not changing in this case, t can be excluded from the calculations. For such a system, the potential energy is stored in the spring and is given by in this case, it can be excluded from the calculations where k is the force constant of the spring and z is the distance from the equilibrium position. The kinetic energy of the system is, as always, where m is the mass of the block and v is the speed of the block. We will also assume that there are no resistive forces; that is, E constant. Consider a harmonic oscillator at four different moments, labeled A, B, C, and D, as shown in the figure (Figure 1). Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A. are given Answer the following questions. Part A Which moment corresponds to the maximum potential energy of the system? View Available Hint(s)