Chapter 13 periodic motion Breaking glas A wineglass can be shattered by sound wave if the wave matches the ollapse of the Tacoma Narrows natural utor tIons the glass suspension bridge in America in 1940 p415
Chapter 13 periodic motion Collapse of the Tacoma Narrows suspension bridge in America in 1940 (p 415)
oscillation SHM Dam ped Forced oscillation oscillation dynamics kinematics Dynamic Kinematics Circle of equation equation reference Energy Superposition of shm
SHM dynamics kinematics Dynamic equation Circle of reference Kinematics equation oscillation Energy Superposition of shm Damped oscillation Forced oscillation
Chapter 13 periodic motion Key Terms periodic motion /oscillation restoring force Amplitude cycle Period Frequency angular frequency simple harmonic motion harmonic oscillator circle of reference Phasor phase angle simple pendulum
Key Terms: periodic motion / oscillation restoring force Amplitude cycle Period Frequency angular frequency simple harmonic motion harmonic oscillator circle of reference Phasor phase angle simple pendulum Chapter 13 periodic motion
Key Terms: physical pendulum Damping Damped oscillation Critical damping overdamping underdamping 〓〓〓 driving force forced oscillation natural angular frequency 删HH resonance chaotic motion chaos
Key Terms: physical pendulum Damping Damped oscillation Critical damping overdamping underdamping driving force forced oscillation natural angular frequency resonance chaotic motion chaos
1. Dynamic equation 1)dynamic equation Ideal model A spring mass system ∑F k x k k +x=0 d=x dt 2 m +02x=0 dt2 2丌 T x=AcOs(Ot+φ)
Ideal model: A. spring mass system 1) dynamic equation kx dt d x m F ma kx = − = = − 2 2 0 2 2 + x = m k dt d x x = Acos(t + ) 0 2 2 2 + x = dt d x m k = 2 T = 1. Dynamic equation
B The Simple Pendulum F = a -mg sing=m-2 s=LO mg sin 8 sindo 0\mg cos 6 Small angle approximation sine × d26 6=0 6=ocos(a+中)
Small angle approximation sin 0 2 2 + = L g dt d B. The Simple Pendulum 2 2 2 2 sin sin dt d g L s L dt d s mg m Ft mat − = = − = = cos( ) = 0 t + l g = 2
C. physical pendulum P409 ∑ t=la d26 mgd sin 8=l dt d6 mgd 6 dt o mod mg sin Ga中测mE
I mgd I mgd dt d dt d mgd I I = = − − = = 2 2 2 2 2 sin C. physical pendulum P409
Example: Tyrannosaurus rex and physical pendulum All walking animals, including humans, have a natural walking pace, a number of steps per minute that is more comfortable than a faster or slower pace. Suppose this natural pace is equal to the period of the leg, viewed as a uniform rod pivoted at the hip joint. A) How does the natural walking pace depend on the length L of the leg, measured from hip to foot? B )Fossil evidence shows that Tyrannosaurus rex, a two-legged dinosaur that lived about 65 million years ago at the end of the cretaceous period, had a leg length L= 3.1 m and a stride length(the distance from one foot-print to the next print of the same foot S=4.0 m Estimate the walking speed of Tyrannosaurus rex. (page 410 EX13-10) Solution:
Example: Tyrannosaurus rex and physical pendulum All walking animals, including humans, have a natural walking pace, a number of steps per minute that is more comfortable than a faster or slower pace. Suppose this natural pace is equal to the period of the leg, viewed as a uniform rod pivoted at the hip joint. A) How does the natural walking pace depend on the length L of the leg, measured from hip to foot? B) Fossil evidence shows that Tyrannosaurus rex, a two-legged dinosaur that lived about 65 million years ago at the end of the Cretaceous period, had a leg length L = 3.1 m and a stride length (the distance from one foot-print to the next print of the same foot ) S = 4.0 m. Estimate the walking speed of Tyrannosaurus rex. (page 410 EX13-10) Solution:
4 Leg Stride length s length Copyright 9 2004 Poarson Education, inc, publishing as Addison Wosley
Solution: 2 T=2丌 L=2038m/s2 2(3.lm) 2.9s 13g S4.0m_14m T2.9
Solution: s m s m g L T 2.9 3(9.8 / ) 2(3.1 ) 2 3 2 2 2 = = = m s s m T S v 1.4 / 2.9 4.0 = = =