# Ch 10 Elasticity Oscillations Problems 3 4 27

Ch. 10 Elasticity & Oscillations • • • Problems: 3, 4, 27, 29. Elastic deformation Hooke’s Law Simple Harmonic Motion (SHM) period & frequency of SHM (sections 3, 4, 7, 8, 9, 10)

Hooke’s Law • The restoring force exerted by an object is proportional to the amount the object has been deformed. • F = -kx • k = elastic constant (N/m) • Ex. SHM-springs used in lab are about 8 N/m. • /

Young’s Modulus: Object with length = L, and area = A. Y is Young’s Modulus which is a measure of stiffness. k = YA/L.

Ex. Young’s Modulus. Area = 0. 1 m^2, L = 25 m, Y = 5000 N/m^2. A pulling force of 100 N applied at each end will cause the length to change by:

Ex. An object with Area = 0. 0001 m^2, L = 1 m, is pulled on both ends by a force of 10 N, causing its length to increase to 1. 4 m. Young’s modulus is:

vibrations • • • Examples: vibrating reed, mass on spring, drum, piano wire, string, … most vibrations are sinusoidal in time, and called “simple harmonic” motions (shm) 6

terminology • • • x: displacement A = amplitude = maximum displacement f: frequency (cycles/s) T = 1/f angular frequency w = 2 pf: (rad/s) k: spring constant (N/m) 7

sinusoidal nature of vibrations 8

A 0. 10 kg mass is hung from a spring with spring constant 8 N/m. Also calculate for 0. 2 kg

SHM Formulas Position: frequency: maximums: 10

SHM Formulas • position: • frequency: • maximums: 11

Ex: SHM Ex: k = 10 N/m, m = 200 grams, A = 10 cm.

Summary • Young’s Modulus • Hooke’s Law • Simple Harmonic Motion • SHM Examples: Mass-Spring System, • Energy Conservation Applied to SHM

natural frequency • lowest frequency an object vibrates with when struck • also called “resonant frequency” • Demo: Driving Tuning Fork • / 14

resonance • absorb max energy: frequency = resonant frequency • example: 256 Hz guitar string resonates when exposed to 256 Hz. • Chilandi plates video 15

Main Results 16

sinusoidal nature of shm • position of blue mass moving on spring turns out to be same as the horizontal position of an object in uniform circular motion. 17

Simple Pendulum small angles 18

- Slides: 18