A mass of 2 kg is attached to a spring, stretching it by 0.98 m. The mass is released from rest at a position 0.1 m below the equilibrium position. Find the equation of motion $x(t)$. Assume $g = 9.8 \text{ m/s}^2$.

A 1 kg mass is attached to a spring with stiffness $k = 5$ N/m. The system is immersed in a medium that offers a damping force equal to 2 times the instantaneous velocity. The mass is initially displaced 1 meter below equilibrium and released with an upward velocity of 2 m/s. Find the equation of motion.

An undamped spring-mass system with $m=1$ and $k=9$ is driven by an external force $F(t) = 12\sin(3t)$. If the system starts from rest at equilibrium ($x(0)=0, x'(0)=0$), find the equation of motion and identify the phenomenon occurring.

A pendulum of length $L = 2.45$ meters is displaced by a small angle of $\theta = 0.1$ radians and released from rest. Find the equation for the angle $\theta(t)$ over time. Use $g = 9.8 \text{ m/s}^2$.

An RLC circuit has $L=1$ H, $R=6$ $\Omega$, $C=1/9$ F, and $E(t)=0$. The initial charge on the capacitor is $q(0)=1$ C, and the initial current is $i(0)=0$ A. Find the charge $q(t)$.

An RLC circuit has $L=0.5$ H, $R=2$ $\Omega$, $C=0.1$ F, and $E(t)=0$. $q(0)=2$ C, $i(0)=0$ A. Find $q(t)$.

A cantilever beam of length $L$ (fixed at $x=0$, free at $x=L$) carries a constant distributed load $w_0$. Find the deflection curve $y(x)$. The governing equation is $EI y^{(4)} = w_0$.

A simply supported beam of length $L$ (pinned at $x=0$ and $x=L$) has a constant load $w_0$. Find $y(x)$.