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 = 0.1m^2, L = 25m, Y = 5000 N/m^2. A pulling force of 100N applied at each end will cause the length to change by:

Ex. An object with Area = m^2, L = 1m, is pulled on both ends by a force of 10N, causing its length to increase to 1.4m. Young’s modulus is:

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

7 terminology x: displacement A = amplitude = maximum displacement f: frequency (cycles/s) T = 1/f angular frequency  f: (rad/s) k: spring constant (N/m)

8 sinusoidal nature of vibrations

A 0.10kg mass is hung from a spring with spring constant 8N/m. Also calculate for 0.2kg

10 SHM Formulas Position: frequency: maximums:

11 SHM Formulas position: frequency: maximums:

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

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

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

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

16 Main Results

17 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.

18 small angles Simple Pendulum