Simple Harmonic Motion YouTube - Color Footage of Tacoma Narrows YouTube - Tacoma Narrows Bridge Collapse "Gallopin' Gertie"

Periodic Motion Motion reoccurs in a regular pattern Simple harmonic motion (SHM): force that restores the object to equilibrium is directly proportional to the displacement Two important measurements:  Period (T): time to repeat one complete cycle  Amplitude: maximum displacement

Mass on a Spring Hooke's Law: force exerted by a spring is directly proportional to the amount the spring is stretched F = -kx PE=(1/2)kx _1.wmv _1.wmv

Springs! Masses & Springs 2.02

Example A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from the end. What is the spring constant? Known: x=0.18m F=56N F=-kx so k=F/x (the negative just means it's a restoring force)‏ k=56N/0.18m = 310 N/m

Example Continued How much PE is stored in the spring? PE=(1/2)kx 2 PE=(1/2)(310N/m)(0.18m) 2 PE=5 J

Now you try it! A 560 N bicyclist sits on a bicycle seat and compresses the two springs that hold it up. The spring constant is 2.2 x 10 4 N/m for each spring. How much is each spring compressed? Know: F=560 N k=2.2 x 10 4 N/m 2 springs F=-kx or x=F/k and since 2 springs x=F/2k X=1.3 x m

Period of a Spring Mass attached to a spring exhibits simple harmonic motion T= 2π√(m/k) Frequency is inverse of period!

Pendulum Object (bob) suspended by a string of length l String exerts tension (force) and gravity exerts force Period of a pendulum: T=2π√(l/g)

Sample Problem A pendulum with length 36.9 cm has a period of 1.22 s. What is the acceleration of gravity at the pendulum's location? Known: T=1.22 s l=0.369 m T=2π√l/g so g=(2π) 2 l (T) 2 g=9.78 m/s 2