Simple Harmonic Motion Wenny Maulina

Energy in SHM The fact that the velocity is zero at maximum displacement in simple harmonic motion and is a maximum at zero displacement illustrates the important concept of an exchange between kinetic and potential energy. If no energy is dissipated then all the potential energy becomes kinetic energy and vice versa, so that the values of (a) the total energy at any time, (b) the maximum potential energy and (c) the maximum kinetic energy will all be equal; that is

Energy in SHM No friction BTW: w2 Energy conservation Energy conservation in a SHM No friction BTW: w2

Energy in SHM kinetic energy E energy energy Energy conservation in a SHM kinetic energy E energy energy distance from equilibrium point Time potential energy

Energy in SHM This graph shows the potential energy function of a spring. The total energy is constant. Figure 14-11. Caption: Graph of potential energy, U = ½ kx2. K + U = E = constant for any point x where –A ≤ x ≤ A. Values of K and U are indicated for an arbitrary position x.

Example Many tall building have mass dampers, which are anti-sway devices to prevent them from oscillating in a wind. The device might be a block oscillating at the end of a spring and on a lubricated track. If the building sways, say eastward, the block also moves eastward but delayed enough so that when it finally moves, the building is then moving back westward. Thus, the motion of the oscillator is out of step with the motion of the building. Suppose that the block has mass m = 2.72 x 105 kg and is designed to oscillate at frequency f = 10.0 Hz and with amplitude xm = 20.0 cm. (a) What is the total mechanical energy E of the spring-block system?

Wave Equation

Wave Equation

Example Tunjukkanlah bahwa 𝑦=𝐴𝑠𝑖𝑛 𝑘𝑥−𝜔𝑡 memenuhi persamaan gelombang dengan menghitung secara eksplisit turunan-turunannya