Physics 321 – Spring 2006Homework #6, Due at beginning of class Wednesday Mar 1.1. [4 pts] A hook is at heightyabove the floor, whereyis constant for all negativetimes:y=y0fort <0. For positive times,yoscillates:y=y0+Asinωtfort >0. A massMhangs from an ideal spring attached to this hook. The mass isat heightxabove the floor. The mass hangs motionless atx=x0=y0-Mg/kfort <0, wherekis the spring constant. Letω0=qk/Mas usual.(a) Find the motionx(t) of the mass fort >0 ifω= 2ω0.(b) Find the motionx(t) of the mass fort >0 ifω=ω0. (You can do this byfirst findingx(t) for arbitraryωand then carefully taking the limitω→ω0; orif you’re chicken, you can setω→ω0in the equation of motion and solve it.)2. [4 pts] A driven harmonic oscillator obeys the equation¨x+x=t(A-t) for 0< t < A. Given the initial conditionsx= ˙x= 0 att= 0,find the subsequent motionx(t) during the time interval 0< t < A.3. [4 pts] Marion & Thornton, problem 3-20 (Same in 4th edition). Do this problemby hand (i.e., using algebra, not using a computer). You need to find the two
This is the end of the preview.
access the rest of the document.