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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.
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Q. Determine v, i, and the power delivered to elements in the network given in Figure. Check whether conservation of power is satisfied by the circuit.
Q. What is Barkhausen criterion? Why is the value of Ab kept slightly greater than 1? The condition |Ab| = 1 is called the Barkhausen criterion. It implies that when |Ab| = 1,
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what is the method to do this project and what material used for?
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