A particle $$\(P\)$$ of mass $$\(2 \mathrm{~kg}\)$$ is attached to one end of a light elastic spring, of natural length $$\(0.8 \mathrm{~m}\)$$ and modulus of elasticity $$\(12 \mathrm{~N}\)$$. The other end of the spring is attached to a fixed point $$\(A\)$$ on a rough plane. The plane is inclined at $$\(30^{\circ}\)$$ to the horizontal. Initially $$\(P\)$$ is held at rest on the plane at the point $$\(B\)$$, where $$\(B\)$$ is below $$\(A\)$$, with $$\(A B=0.3 \mathrm{~m}\)$$ and $$\(A B\)$$ lies along a line of greatest slope of the plane. The point $$\(C\)$$ lies on the plane with $$\(A C=1 \mathrm{~m}\)$$, as shown in Figure 3. The coefficient of friction between $$\(P\)$$ and the plane is 0.3 After being released $$\(P\)$$ passes through the point $$\(C\)$$. Find the speed of $$\(P\)$$ at the instant it passes through $$\(C\)$$. (7)

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