Applied Maths - Mechanics 43

The ends of a light elastic string, of natural length 2a, are fixed to two points in a horizontal line at a distance 2a apart.

When a particle of mass m is attached to the midpoint of the string and hangs in equilibrium, the two parts of the string are inclined at 45 degree to the horizontal. The particle is then displaced in a vertical line through a small distance x.

(a) Find the modulus of elasticity of the string.

(b) Find the force tending to restore the particle to its original position neglecting (x/a)^2 and higher power of (x/a) .

(c) Show that, if released, the particle will execute small oscillations with the same period as that of a simple pendulum of length 2a[3 - (2)^0.5 ] / 7 .