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## Homework Statement

Consider an underdamped harmonic oscillator (Q > 1/2) with a sinusoidal driving

force Focos(ωdt).

(a) (5 pts) By using differential calculus find ωd that maximizes the displacement amplitude.

(b) (7 pts) By using differential calculus find ωd that maximizes the velocity amplitude.

## Homework Equations

x(t)= (fo/m)/sqrt([wo^2-wd^2]^2+(gama(wd)^2)

## The Attempt at a Solution

I know what the end solution will be and the general theory behind this but I am unsure how to proceed. I am unsure how to prove the point at which it is the maximum.