Simple Harmonic Motion

Types of Motion Periodic Motion Motion which repeats itself Intervals of Time  Ex. watch, heart pumping Oscillatory Motion Motion over the same path Ex. Drive to school

Simple Harmonic Motion Periodic, oscillatory motion under the influence of a restoring force Repeated pattern – cycle Time for one cycle – period (T) # of cycles / time – frequency (f) = 1 / T  Ex. Pendulum – Galileo (chandelier and pulse in church at Pisa) said they had a constant period  Ex. Body on a spring – Newton

Body on Spring Restoring Force Spring – Elastic Restoring Force Can we use Galileo’s Equations? No! Acceleration not constant

Mass on Spring and Pendulum Is T dependent on amplitude? No Is T dependent on mass of bob? Not for pendulum Yes for spring How do we know this? T pendulum = 2π√(l/g) T = period, l = length, g = gravity T spring = 2π√(m/k) T = period, m = mass, k = spring constant

Pendulum Examples How would you adjust a Grandfather clock? T pendulum = 2π√(l/g) Which has a faster stride, a centipede or a dog? Shorter legs vs. longer legs Small l  small T Large l  large T

Spring Equations T spring = 2π√(m/k) T = period, m = mass, k = spring constant Large mass  large T Small mass  smaller T Hooke’s Law: F = -kx - or - k = -F / x F spring = opposite weight  + x = distance stretched by spring  - k = positive # in N/m or lbs/ft

F = max down v = 0 F = 0 v = max down F = 0 v = max up F = max up v = 0 F = max down v = 0 At top At bottom