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

**Question description**

# 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.

## Tutor Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors