1. Simple Harmonic Motion
Wenny Maulina

2. 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

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

4. 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

5. Energy in SHM
This graph shows the potential energy function of a spring. The total energy is constant.
Figure 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.

6. 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?

9. Wave Equation

10. Wave Equation

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