3 Fig. 3 shows the fixed points A and F which are 9.5 m apart on a smooth horizontal surface and points B and D on the line AF such that \(\mathrm { AB } = \mathrm { DF } = 3.0 \mathrm {~m}\). A small block of mass 10.5 kg is joined to A by a light elastic string of natural length 3.0 m and stiffness \(12 \mathrm { Nm } ^ { - 1 }\); the block is joined to F by a light elastic string of natural length 3.0 m and stiffness \(30 \mathrm { Nm } ^ { - 1 }\). The block is released from rest at B and then slides along part of the line AF . The block has zero acceleration when it is at a point C , and it comes to instantaneous rest at a point E .
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\caption{Fig. 3}
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- Find the distance BC .
At time \(t \mathrm {~s}\) the displacement of the block from C is \(x \mathrm {~m}\), measured in the direction AF .
- Show that, when the block is between B and \(\mathrm { D } , \frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } = - 4 x\).
- Find the maximum speed of the block.
- Find the distance of the block from C when its speed is \(4.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the time taken for the block to travel from B to D.
- Find the distance DE .