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Pearson Edexcel IAL Mathematics M3.3.3 Oscillations attached to elastic strings or springs

Practise elastic-string oscillations where the particle moves in the string direction and SHM methods give speed, time and validity checks.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • derive ẍ=-ω^2x for motion along the elastic string or spring
  • justify continued SHM by comparing the amplitude with the extension needed to stay taut
  • use SHM speed or displacement formulae to find the speed at a named point

M3.3.3 - Oscillations attached to elastic strings or springs question 1

[Maximum number: 3]

The fixed point A is vertically above the fixed point B, with A B=3 l

A light elastic string has natural length l and modulus of elasticity 4 m g One end of the string is attached to A and the other end is attached to a particle P of mass m

A second light elastic string also has natural length l and modulus of elasticity 4 m g One end of this string is attached to P and the other end is attached to B.

Initially P rests in equilibrium at the point E, where AEB is a vertical straight line.

Find, in terms of g and l, the speed of P when it is 18l\frac{1}{8} l below E.

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