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110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所系統控制組:控制系統(A)#100776
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4.(30%) Consider Figure 3 with
(4) (5%) Design a first-order controller C(s) to assign all closed-loop poles at s=-2.
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(5) (10%) Design a controllersuch that the system has a phase margin of greater than 45° and a bandwidth of less than s+p 20 rad/sec. s(s-9)'
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1. The 2020 Nobel Prize in Physics was awarded jointly to Roger Penrose from Britain, Reinhard Genzel from Germany and Andrea Ghez from the US. Pease describe their discoveries in brief. (10%)
#422099
2. Calculate the wavelength in nm of electrons which have been accelerated from rest through a potential difference of 54V. (15%)
#422100
(a) What additional quantum numbers are needed to specify fully an atomic quantum state and what physical quantities do they quantify? (10%)
#422101
(b)List the allowed quantum numbers for n = 1 and n = 2 and specify fully the electronic quantum numbers for the ground state of the Carbon atom (atomic number Z=6).(10%)
#422102
(a) Modelling this as a one-dimensional infinite square well, determine the value of the quantum number n if the marble is initially given an energy of 1 mJ. (10%)
#422103
(b)Calculate the excitation energy required to promote the marble to the next available energy state. (10%)
#422104
5. Use the uncertainty principle to make an order of magnitude estimate for the kinetic energy (in eV) of an electron in a hydrogen atom. (15%)
#422105
(a) The Compton shift at this angle. (8%)
#422106
(b) The energy of the scattered X-ray. (6%)
#422107
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110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所系統控制組:控制系統(A)#100776
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