When a rubber-band is stretched by a distance x

• Oscillation Waves

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber band by L is

1. aL²/2 + bL³/3
2. (aL² + bL³)/3
3. aL² + bL³
4. (aL²/2 + bL³/3)/2

Answer

F = ax + bx²

dw = F dx

w = _o∫^L (ax + bx²)dx

w = aL²/2 + bL³/3

The correct option is A.