Act14_sol

# Act14_sol - 2/18/05 Activity 14 Solutions: Sensitive...

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2/18/05 1 Activity 14 Solutions: Sensitive Systems and Computer Modeling 14.1 Sensitivity of Systems to Initial Conditions 1) Predictable and unpredictable systems Your instructor will demonstrate a simple pendulum, starting its motion several times. a) Is it possible to predict the motion of this pendulum each time? Yes, it swings back and forth in a regular pattern. b) What set of laws govern the motion of the pendulum? Newton’s laws of gravitational force and motion c) Your instructor will demonstrate a modified pendulum that includes a spring. Does this pendulum also follow Newton’s Laws? Yes Can you predict the motion of this pendulum? No, it moves unpredictably. d) When the second pendulum is repeatedly set in motion with as close to identical conditions as possible, does this pendulum behave the same each time? No How does the spring change the character of the pendulum? The spring makes the second pendulum sensitive to variations in the initial conditions. 2) Deterministic systems As we have seen, both predictable and unpredictable systems follow Newton’s Laws. a) What is the term for a system for which we know the laws governing the system’s behavior? A deterministic system b) What is the relationship between successive events in a deterministic system? In a deterministic system, each successive event may be determined from previous events. c) Are there any systems in nature that are not deterministic? No. If we know all of the equations that govern the behavior of any system, the subsequent behavior of that system can be determined by previous events. 3) Sensitive and non-sensitive systems and initial conditions Next, we examine the difference between predictable and unpredictable systems. a) Place the ice cream cone upside down. Tilt the cone slightly to the right side and release it. What happens? The cone returns to its initial position. b) Is the behavior of the cone predictable?

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2/18/05 2 Yes, if the cone is tilted only slightly, it always returns to its initial position. c) Change the initial conditions by tilting the cone to the left or toward you or away from you and then release the cone. Is the final position of the cone the same in each case? Yes, the cone returns to its initial position no matter in which direction it is slightly tilted. d) Is the final position of the cone sensitive to your choice of initial conditions? No.
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## This note was uploaded on 06/11/2011 for the course PHYSICS 104 taught by Professor Staff during the Winter '11 term at Ohio State.

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Act14_sol - 2/18/05 Activity 14 Solutions: Sensitive...

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