# Solution 3 - Theoretical Question 3 Solutions Page 1/6...

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Unformatted text preview: Theoretical Question 3 / Solutions Page 1/6 Theoretical Question 3: Scanning Probe Microscope 1. Answers (a) 2 2 2 2 2 2 ) ( ω ω ω b m F A + − = and ) ( tan 2 2 ω ω ω φ − = m b . At ω ω = , ω b F A = and 2 π φ = . (b) A non-vanishing dc component exists only when i ω ω = . In this case the amplitude of the dc signal will be i R i V V φ cos 2 1 . (c) 2 2 1 2 ω b V c c R at the resonance frequency ω . (d) 18 10 7 . 1 − × = ∆ m kg. (e) 2 / 1 2 3 1 ' − = ω ω ω m c . (f) 3 / 1 ∆ = ω ω m qQ k d e = d 41 nm. Theoretical Question 3 / Solutions Page 2/6 2. Solutions (a) [1.5 points] Substituting ) sin( ) ( φ ω − = t A t z in the equation t F z m dt dz b dt z d m ω ω sin 2 2 2 = + + yields, t A F t m t b t m ω φ ω ω φ ω ω φ ω ω sin ) sin( ) cos( ) ( sin 2 2 = − + − + − − . (a1) Collecting terms proportional to t ω sin and t ω cos , one obtains { } cos cos sin ) ( sin sin cos ) ( 2 2 2 2 = + − − + − + − t b m t A F b m ω φ ω φ ω ω ω φ ω φ ω ω (a2) Zeroing the each curly square bracket produces ) ( tan 2 2 ω ω ω φ − = m b , (a3) 2 2 2 2 2 2 ) ( ω ω ω b m F A + − = . ....
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Solution 3 - Theoretical Question 3 Solutions Page 1/6...

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