phy53 lect dr. brown 16 november 2010 curve balls -- baseball discussion -- golf balls...dimpled surface; compare to ping pong ball leading to Young's Modulus atoms modeled like connected by springs [discussion of similarity -- Leonard-Jones potential -- consider Taylor series expansion about the minimum] single chain; two chains; block of material with cross sectional area... F_{restoring} = - Y A/L \Delta L = -"k_eff" \Delta L Y = young's modulus = stress over strain = (F/A)/(\Delta L /L) explains linear response limit, elastic limit[permanent deformation] and fracture limit Another material response -- push rectanglular cross section at top -- shear stress and strain Shear modulus = shear stress / shear strain = (F/A) / (\Delta x /L) finally -- "Bulk modulus" increase pressure -- response is change in volume large bulk modulus => low compressibility We can really understand springs now and where, from microscopic view of matter, Hooke's Law comes from-- so, solve -- mass on a spring F_x = -kx = m a = m \frac{d^2 x}{dt} Simple Harmonic Oscillator Equation \frac{d^2 x}{dt^2} + \frac{k}{m} x = 0 solve it Euler equation...real part ... x(t) = x_o cos (\omega t + \delta) next -- pendulum ... nonlinear diffy q so, make small angle approximation sin(\theta) approx \theta