Simple Harmonic Motion Chapter 11 Part 1

(measured in N/m, N/cm or lb/in) Hooke’s Law Hooke’s Law applies to springs, bows etc. Every spring has a Hooke’s constant for that spring “k” It is a measure of the strength of the spring (measured in N/m, N/cm or lb/in) To extend or compress a “Hookean spring “ with a constant “k” from equilibrium Fext = kx X = displacement from equilibrium

Frestore = - kx Restoring Force A Hookean spring will pull back with an equal but opposite force that tries to restore equilibrium Frestore = - kx

Simple Harmonic Motion When an extended or compressed spring is released the restoring force will try to restore equilibrium. Momentum makes it overshoot So it tries again, overshoots ,tries again..a repeating or Simple Harmonic Motion Stings on musical instruments, & Pendula also move in SHM

Measuring SHM Every SHM has the following measurable properties: Amplitude(A): Maximum displacement from Equilibrium. Period(T): The time it takes to complete a cycle Frequency (f): The number of cycles in one second (Measured in “Hertz” (Hz) or “cycles/second”)

Period of a Simple Pendulum The period (T) of a pendulum with a length (L) on a planet with an acceleration do to gravity (g) is:

The Period of a Mass-Spring System The Period of a mass (m) attached to a spring with strength of (k) is: