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HW2 Spring 2011

HW2 Spring 2011 - TA's Name Section Your Name Physics 2214...

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Physics 2214 Assignment 2 Concepts: oscillations damped oscillations restoring forces driven oscillatons and resonance simple harmonic motion damping regimes force law for SHM decay time and resonance width damped oscillations power in driven oscillations Reading: Lecture notes 1, 2 and 3; Y&F, Vol. 1, Chapters 13 and 15 Assignment: Due in homework boxes opposite 125 Clark Hall before 430 pm on Tuesday February 8. Please turn in this sheet stapled to the top of your work. 1. Equilibrium. Shown below is a plot of F ( x ) versus x , the force experienced by a particle in the x direction as a function of its position x . (a) At which point or points may the particle undergo simple harmonic motion, when it is initially displaced by a small Δ x ? (b) Which point or points correspond to an unstable equilibrium position? 2. SHM. A small body of mass m=0.02 kg is attached to a spring of spring constant k=5 N/m, and is undergoing simple harmonic motion of amplitude x m =10 cm about x=0. At t=0, the mass is at x= 0 cm. (a) Write an expression for the position x(t) of this mass as a function of time, giving numerical values for all constants. (b) For at least two periods of the motion, draw the following graphs, with each new graph below the previous one, using the same time scale in all of the graphs. Label the axes with numbers. (i) x vs t (position versus time). TA's Name:____________________ Section: ____ Your Name: _________________________________ Physics 2214, Spring 2011 1 Cornell University

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(ii) v x vs t (velocity versus time). (iii) a x vs t (acceleration versus time). (iv) K vs t (kinetic energy versus time). (v) U vs t (spring potential energy versus time). (vi) E mech vs t (total mechanical energy = U + K versus time). 3. Ground motion in earthquakes. On January 12, 2009, a magnitude 7.0 earthquake struck Haiti near its capital Port-au- Prince. Approximately 230,000 people died and 1,000,000 were made homeless. 250,000 residences and 30,000 commercial buildings collapsed or were severely damaged. Six weeks later on February 27, 2009 a magnitude 8.8 earthquake struck Chile. The entire city of Concepcion moved 10 feet to the west. Despite releasing nearly 100 times as much energy as the Haiti quake, only 500 people died and damage was comparatively modest. Why?
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HW2 Spring 2011 - TA's Name Section Your Name Physics 2214...

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