# How do I analyze y(x) and find the maximum dimensionless amp of ymax .

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# How do I analyze y(x) and find the maximum dimensionless amp of ymax and at what dimensionless frequency xmax it is reached.?

oscillations driven by a periodic force F=F_0 cos(w(omega)t). To analyze the expression for the amplitude of a driven oscillator, we will rewrite it in dimensionless form.

Preliminary stuff. Step 1: show that a constant force F_0 applied to the oscillator will stretch the spring by A_0=F_0/(m w_0 ^2) where w_0 is the natural frequency of the oscillator. Length A_0 will be our “meter stick” in this problem, and we will measure the amplitude of oscillations in terms of a dimensionless quantity y=A/A_0.

Step 2: following the class notes, express y in terms of a dimensionless “frequency” x=w/w_0 and the quality factor Q.

Now, the actual problem. Analyze y(x) and find the maximum dimensionless amplitude ymax and at what dimensionless frequency xmax it is reached.

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