3. Energy.

On a horizontal surface, we have a massless spring that is connected to an object

with mass m. The spring constant is k. The friction of this object with the surface is

the product of a constant b with the velocity of this object. Consider 1-dimensional

motion of this object in x direction: when the object is located at x2, the spring has

no force on the object. Say initially the object's location is x1, with a velocity of V₁.

There is no other external forces like driving force or so. Assume no static friction.

Question (a): After very long time, how much heat will be generated due to the

dissipation caused by the friction of this object? Consider from the energy

perspective.

Question (b): Prove your answer in (a) above, using the fact that the work done by a

force is equal to the integral of this force over distance. Hint: Consider the equation

of motion; Also, (dv/dt) dx =dv*v=vdv