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P H Y S I C SChapter 7: Waves and Vibrations

Section 7A: Hooke's Law and SHM of a Mass-Spring System

Discovered the cellHookes Law

(1635-1703)Hookes Law Demo

Robert Hooke

Hookes LawSpring force is directly proportional to displacement of spring

spring constant slope = kHookes Law EquationSimple Harmonic Motion (SHM)SHM = periodic vibration about an equilibrium pointAmplitude = max displacement

xo = 0 equilibriumamplitude+xamplitude-xMax force occurs at amplitudeZero force occurs at equilibrium Force

maxforce xo-x+xmaxforce zeroforceMax velocity occurs at equilibrium Zero velocity at amplitudeVelocity

xo-x+xmaxvelocityzerovelocityzerovelocityPeriod of a Mass-Spring SystemPeriod of a Mass-Spring SystemPeriod is independent of amplitude

In-Class Problem #1Determine the mass suspended at rest from the spring.

m = 30.6 kg

x = -1.2 mk = 250 N/m In-Class Problem #2A 2 kg mass is pulled back 0.5 m from equilibrium with a force of 60 N. Determine the period of oscillation.

k = 120 N/mT = 0.81 s

AssignmentProblem Set 7A7A-7B Quiz (Simple Harmonic Motion)