A nonlinear spring has a restoring force which is proportional to the cube of the displacement x The period T of oscillation from an initial displacement a is given by Use the substitution x 2 a 2 sin to transform this integral to and use the trapezium rule to evaluate this integral T 42 D 0 1 (a x...

1 I 4 ax x2a sine 2xdx a cos de dx a cos 2sin 12 T 42 dx do ...

A nonlinear spring has a restoring force which is proportional to the cube of the displacement x.

Question:

A nonlinear spring has a restoring force which is proportional to the cube of the displacement x. The period T of oscillation from an initial displacement a is given by

T = 42 D. 0 1 (a* - x) - d.x Use the substitution x² = a² sin θ to transform this integral to

T= T = 22/0 a where Use the recurrence relation (r + 1)F(r) = (r + 2)F(r + 2) F(r) = to show that T= **/2 0 and use the trapezium rule to evaluate this integral.