IIT-JEE 1999 Screening

The coordinates of a particle moving in a plane are given by x(t) = a cos(pt) and y(t) = b sin(pt) where a, b (< a) and p are positive constants of approprite dimensions. Then

A particle free to move along the x-axis has potential energy given by \(U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]\) for \(- \infty \le x \le - \infty\), where k is a positive constant of appropriate dimen...

A spring of force-constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of