Simple Harmonic Motion

About the lecture

In this mini-lecture, we introduce simple harmonic motion (SHM). As we move though this mini-lecture, we consider: (i) pendulums and springs, which both exhibit SHM; (ii) gravity and elasticity as suitable restring forces that allow for SHM in the pendulum and spring, respectively; (iii) SHM of a mass on a spring with a restoring force given Hooke’s Law F = kx; (iv) the relationship between the potential energy of a mass on a spring, which is quadratic, and the force (F = kx), which is linear; (v) the equation for acceleration of SHM systems, where we introduce angular frequency, natural frequency, and period; (vi) the equation for the acceleration of SHM, and relate it back to the displacement equation derived in mini-lecture 2; (vii) the period and frequency of the pendulum, checking the dimensions and going over an example; (viii) the period of a mass on a spring, and check the dimensions; and (ix) the relationship between the period of the pendulum and a mass on a spring, which gives an expression for the spring constant.

About the lecturer

Giles Hammond is a Professor of Experimental Gravitational Physics at the University of Glasgow. His research interests focus on the development of fused silica suspension systems for gravitational wave detectors. He has made significant contributions to the development of the monolithic stages of quadruple pendulums used in the process of updating the components used in the Laser Interferometer Gravitational-Wave Observatory (LIGO) into the experiment now deemed Advanced LIGO (aLIGO). During this process, he led the installation of several suspensions at both the Hanford and Livingston aLIGO sites. This improved precision of aLIGO contributed to the first direct detection of gravitational waves in 2015, which led to the 2017 Nobel Prize in Physics.