(Solved): The values of mass \( m \), spring constant \( k \), dashpot resistance \( c \), and force \( f(t) ...

The values of mass \( m \), spring constant \( k \), dashpot resistance \( c \), and force \( f(t) \) are given for a mass-spring-dashpot system with external forcing function. Solve the initial value problem and construct the graph of the position function \( \mathrm{x}(\mathrm{t}) \) \[ \begin{array}{l} m x^{\prime \prime}+c x^{\prime}+k x=f(t), x(0)=x^{\prime}(0)=0 \\ m=1, k=49, c=0 ; f(t)=\sin 3 t \text { if } 0 \leqq t \leqq 2 \pi, f(t)=0 \text { if } t>2 \pi \end{array} \] Solve the initial value problem \[ x(t)= \]