can you please help me solving these

4.4 Mechanical and Electrical Vibrations. Problems from pages 262264 1. Assume the system described by the equation mg" + 7y' + kg = D is either critically damped or overdamped. Show that the mass can pass through the equilibrium position at most once, regardless of the initial conditions. 20 points 2. Assume that the System described by the equation my\" + W + kg = 0 is critically damped and that the initial conditions are y(0) = ya and y'(0) = on. if co = 01 show that y -+ 0 as t -> 00 but that y is never zero. If ya is positive, determine a condition on no that will ensure that the mass passes through its equilibrium position after it is released. 20 points 3. A series circuit has a capacitor of 0.25 x 106 fared and an inductor of 1 henry. If the initial charge on the capacitor is 103 coulomb and there is no initial current, find the charge on the capacitor at any time t. 20 points 4. A mass weighing 8 lb stretches a spring 1.5 in. The mass is also attached to a damper with coeicient 7. Determine the value of 7 for which the system is critically damped. Be sure to give the units for 1e. 20 points 3 r\" .l I .I - I I" I. r I 'I -I 4' r I - l' a