phy53 lecture dr. brown 18 november 2010
sho treated
spring mass (frictionless)
small angle pendulum
torsional spring --
\tau = - k \theta torque = - constant * angle of twist = I \alpha
get SHO diffy q !
physical pendulum --
hoop swinging about pivot on the top of the hoop
rod swings with pivot about end
compared to walking -- modeling a leg with rod [foot at end] pivoted at hip
note the "process" for all these SHO problems
discussion of initial conditions -- addressing question(s)
physics as gardening or cooking...
neat coordinate change to transform non-homogeneous diffy q to homogenous diffy q about equilibrium position
now -- mass on spring inserted into fluid [damping force] --- leads to damped harmonic oscillator
underdamped, critically damped, overdamped
real life -- shock absorbers in car -- "good" = slightly underdamped
next driven harmonic oscillators