22 6. A light elastic string, of natural length l and modulus of elasticity 2mg, has one end attached to a fixed point A and the other end attached to a particle P of mass m. The particle P hangs in equilibrium at the point O. (a) Show that AO = 3 2 l (2) The particle P is pulled down vertically from O to the point B, where OB = l, and released from rest. Air resistance is modelled as being negligible. Using the model, (b) prove that P begins to move with simple harmonic motion about O with period π 2l g (5) The particle P first comes to instantaneous rest at the point C. Using the model, (c) find the length BC in terms of l, (4) (d) find, in terms of l and g, the exact time it takes P to move directly from B to C. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
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Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
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