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1. Find the general solution y(t) of the ordinary di erential equation
where ω is a non-negative constant. (Consider the ω = 0 and ω > 0 cases separately).
2. Use Laplace transform to solve the following di erential equation for y(t):
given that y(0) = 0 and y'(0) = 2.3. Consider the following partial di erential equation for u(x; t)
(a) If is a function of t, derive two ODEs by separation of variables.
(b) If is a function of x, derive two ODEs by separation of variables.
A squirrel-cage inductionmotor operates at a slip of 0.05 at full load. The rotor current at starting is five times the rotor current at full load. Neglecting stator resistance and
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Q. Design the high-pass filter shown in Figure (by determining C) to have a half-power frequency of 1 MHz.
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