Hooke’s Law and Simple Harmonic Motion

Waves

In this course, Professor Steven Balbus (University of Oxford) explores waves. In the first mini-lecture, we introduce Hooke’s Law and solve for a mathematical solution that reveals the concept of Simple Harmonic Motion. In the second mini-lecture, we use a model of many masses on springs to understand properties of waves, including transverse and longitudinal waves, amplitude, wave number, wavelength, waves described in space and time, and wave velocity. The third mini-lecture discusses sound waves and water waves, including examples of sound waves in various mediums with various frequencies and tsunami waves. In the fourth mini-lecture, we give an overview of light waves and electromagnetic radiation. The fifth mini-lecture introduces constructive and destructive wave interference, as well as two-source interference. In the sixth mini-lecture, we turn towards diffraction, detailing Huygens' Construction used to determine the angles at which nulls in a wave appear in order to discuss a few examples with familiar objects. In the seventh mini-lecture, we introduce dispersive waves and go through two examples: surface water waves in deep water and waves such as FM radio waves passing through the Earth’s ionosphere. In the eighth mini-lecture, we briefly explore waves in modern physics, discussing Einstein’s photoelectric effect and the wave-like properties of particles, including photons (light particles).

Hooke’s Law and Simple Harmonic Motion

In this first mini-lecture, we introduce Hooke’s Law, F = -kx. In particular we: (i) equate Hooke’s Law to F = ma and rearrange to arrive at a(t) = -(k/m)x(t); (ii) solve for x(t) with a backwards approach that involves understanding the circular motion of a point mass; and (iii) connect this circular displacement of the point mass to the concept of Simple Harmonic Motion.