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Problem 3: The motion of critically damped and overdamped oscillator systems is hardly "oscillatory". (a) To illustrate this, prove that a critically damped oscillator passes through the origin x = 0 at most once, and determine the relationship between the initial conditions xo and vo that is required for the oscillator to pass through the origin. (b) Do the same thing for the overdamped oscillator.

Problem 3: The motion of critically damped and overdamped oscillator systems is hardly "oscillatory". (a) To illustrate this, prove that a critically damped oscillator passes through the origin x = 0 at most once, and determine the relationship between the initial conditions xo and vo that is required for the oscillator to pass through the origin. (b) Do the same thing for the overdamped oscillator.

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Problem 3: The motion of critically damped and overdamped oscillator systems is hardly "oscillatory". (a) To illustrate this, prove that a critically damped oscillator passes through the originx = 0 at most once, and determine the relationship between the initial conditions To and vo that is required for the oscillator to pass through the origin. (b) Do the same thing for the overdamped oscillator.
Transcribed Image Text:Problem 3: The motion of critically damped and overdamped oscillator systems is hardly "oscillatory". (a) To illustrate this, prove that a critically damped oscillator passes through the originx = 0 at most once, and determine the relationship between the initial conditions To and vo that is required for the oscillator to pass through the origin. (b) Do the same thing for the overdamped oscillator.
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