Question

1. a mass of 3 slugs (this is the English unit for mass, a pound is a force) is attached to a vertical spring with a spring constant of k = 9 lbs/ft. The string has a damping constant of beta = 6 lb * s/ft. The mass is pulled 1 ft below its equilibrium position and released. Determine the equation of motion for the mass. you may use any method you know to solve this problem.
hint: y'(0) = 0

2. a capacitor whose capacitance is 2 / 1010 farads, an indicator whose coefficients of inductance is 1 / 20 Henry, and a resistor whose resistance is 1 ohm are connected in series. If at t=0, I = 0 and the charge on the capacitor is 1 coulomb, calculate the charge and the currents in the current due to the discharge of the capacitor when t=0.01 seconds. An external battery provides a voltage of E(t)= 50 sin(120t) is provided.

Answer 1

I am attaching the solution in a image file,
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I hope the solution is clear and siatisfactory. Any confusion can be cleared by asking.

Thank you.