(Solved): 1.2 The underdamped system Solve the mass-spring-dashpot model (2) for the following values of par ...

1.2 The underdamped system Solve the mass-spring-dashpot model (2) for the following values of parameters: \( m=1, k=2 \), and \( c=2 \), if the initial condition is that the mass is carefully released from the displacement \( x(0)=1 \), so that the initial velocity is zero, i.e., \( \frac{d x}{d t}(0)=0 \). Plot the solution \( x(t) \). 1.3 The critically damped system Solve the mass-spring-dashpot model (2) for the following values of parameters: \( m=1, k=1 \), and \( c=2 \), if the initial condition is that the mass is carefully released from the displacement \( x(0)=1 \), so that the initial velocity is zero, i.e., \( \frac{d x}{d t}(0)=0 \). Plot the solution \( x(t) \).