Non-Linear and Chaotic Oscillations of the Forced Pendulum 1. Assume that the un

Question

Non-Linear and Chaotic Oscillations of the Forced Pendulum

1. Assume that the unforced oscillations of a pendulum have a small angle oscillation period= 0.9 seconds. The oscillation period of this pendulum for an amplitude of 170 degrees could be:
a. 0.5 seconds
b. 0.8 sec
c.0.9 sec
d. 1.0 sec

2. Assume that an oscillator is driven by a sinusoidal force. Candidate forces that restore this oscillator to the equilibrium position are listed below. Choose the restoring force that could possibly produce chaotic oscillations. K is a constant. There may be more than one correct answer choice in these options.
a. -kx
b. -kx^2
c. -ksinx
d.-k(sinx)^2

Explanation / Answer

Assume that an oscillator is driven by a sinusoidal force. Candidate forces that restore this oscillator to the equilibrium position are listed below. Choose the restoring force that could possibly produce chaotic oscillations. K is a constant. Then restoring force is F = -k(sinx) If x is very small then sinx is approximately equal to x. Then in that case F = -kx

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