Applications of second order differential equations

Mechanical Vibrations
A spring has a weight of 5kg attached to the end of it. The spring has a natural length of 0.3m and a force of 35 newtons is required to stretch the spring to a length 0.8m. If the spring is stretched to 0.5 meters and then released (with zero initial velocity), then what is the position of the mass at time $t$ ?
Suppose that a hydraulic shock has a spring constant of 40 newtons per meter. There is a weight of 10kg attached to the end of the shock, and the shock has a resting length of 0.5 meters.
1. What is the position of the mass at time $t$ if the hydraulic shock has a damping constant of $c=50$ , with an initial positions of 0.75 meters, and an initial velocity of 0 $m/s$ ?
2. What is the position of the mass at time $t$ if the hydraulic shock has a damping constant of $c=40$ , with an initial position of 0.5 meters, and an initial velocity of 5 $m/s$ ?
3. What is the position of the mass at time $t$ if the hydraulic shock has a damping constant of $c=20$ , with an initial position of 0.3 meters, and an initial velocity of -0.3 $m/s$ ?
Electrical Circuits

Find the charge at time $t$ for an electrical circuit with a resistor that has a resistance of $R=14 \Omega$ , an inductor with $L=2H$ , a capacitor with $C=0.05 F$ , and a battery with charge $E(t)=8$ $\sin(2t)$ . The initial charge is $V=\frac{22}{29}$ coulombs, and the initial current is $I=\frac{6}{29}$ amps.