Prove, by integration, that the work done in stretching an elastic string, of natural length / and modulus of elasticity A, from length / to a length 1+x is 21
A particle of mass m is suspended from a fixed point O by a light elastic string of natural length I. When the mass hangs freely at rest the length of the string is 131. The particle is now held at
rest at O and released. Find the greatest extension of the string in the subsequent motion.
By considering the energy of the system when the length of the string is 1+x and the velocity of the particle is v explain why
mv² = mg (l+x) - 6mg =
Hence show that the kinetic energy of the particle in this position may be written as
mg
where a and ? are positive constants which must be found. Hence deduce that the maximum kinetic energy of the particle during the whole of its motion occurs when it passes through the equilibrium position.