Kirchoff's Laws; Mass-Spring Equation

Consider a basic electric circuit with a resistor, capacitor, and inductor and input voltage V(t). It follows Kirchoff's Laws that the charge on the capacitor Q = Q(t) solves the differential equation: {see attachment}, where L (inductance), R (resistance), and C (capacitance) are positive constants (depending on material). The current in the circuit is the rate of change of the charge: I(t) = Q'(t). (a) Compare this to the mass-spring equation. What plays the role of the mass, spring constant, damping coefficient, displacement, velocity, external forcing? (b) Suppose a given circuit has no input voltage (V(t)=0) and a positive initial charge Q(0) = Qo > 0. Find a condition on R > 0 so t... click for more

System of Equations - Matrix Form; Eigenvalues

Consider the attached system of equations. (a) Write the system in the given matrix form {see attachment} (b) Determine the eigenvalues of A in terms of the parameter {see attachment} (c) The qualitative nature of solutions depends on .... **Please see attachment for complete set of questions. Also, please note: no computer, no calculator. Show how you would have done things by hand. Thanks!

Equivalent Systems (Write Given Second Order Equation...)

Write the given second order equation as its equivalent system of first order equations {see attachment for details}

Equivalent Systems

Write the given second order equation as its equivalent system of first order equations {see attachment for details}

Equivalent Systems

Write the given second order equation as its equivalent system of first order equations {see attachment for details}