A block of mass \(m\) is gently attached to the spring and released at time \(t=0\), when the spring has its free length. During subsequent motion of the block, the displacement of the block \(x\) with respect to time \(t\) is considered. Find \[\displaystyle\int_0^3 x ~\mathrm{d}t\]

**Details and Assumptions**

- Neglect air resistance.
- \(k\) is the spring constant.
- \(m = 10\text{ kg},k = 34 \text{ Nm}^{-1}, g = 9.8 \text{ ms}^{-2}\)

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