Lab 07 Expectations

Submit Plots: 1, 3, 4, 6

1. - Pplane plot of v vs. y, and pplane plot of y vs. t.
   - Estimate the amplitude and period from the graph.
   - Would you consider this a slow or fast oscillation?
   
   
2. - Find the general solution.
   - Find the particular solution using y(0) = 3 and y'(0) = -1.
   - Find exact value for period.
   
   
3. - Will a stiff spring oscillate faster or slower?
   - Test your hypothesis by changing the ks value on your graphs.
   - State your results.
   
   
4. - Use graphs to estimate the max. displacement for the values listed of w.
   - Construct a graph of max displacement as a function of w.
   - (MS Office Excel might be a good program to store results and produce a graph.)
   
   
5. - Solve equation (2) with w=.5 and given initial conditions.
   - Use your solution to prove the peaks lie on a straight line.
   - What is the slope of this line?
   
   
6. - Similar to #4, except µ=.3.
   - Use graphs to estimate the max. displacement for the values
   - Find the maximum displacement to the nearest hundredth.
   - Construct a graph of max displacement as a function of w.i
   
   
7. Discussion:
   - What is resonance? Discuss the effect of resistance on resonance. Does adding resistance change the resonant frequency? If so, how?
   - Graph by hand: Plot the approximate graphs from four and six again on one plot. Then sketch what the frequency response curve might look like for a smaller value of µ on that plot. Where would you expect the max to be? Why?