Answer to Question #248908 in Classical Mechanics for Gabgan

Question

Describe the type of spring "constant" needed to produce a constant restoring force like curve (a) in fig. 7-1.

Answer 1

We know, the relationship is,

$F=kx$

Now, as $x$ increases for constant value of $k$ , $F$ will also increase. But we don't want it. We want a constant $F$ value for all the values of $x$ . So with increasing $x$ , we have to decrease k with such a value so that the multiplication of $k$ and $x$ (i.e, $k×x=F$ ) remain constant. So with increasing $x$ , we have to decrease the value of $k$ with the stretch.

Hence ;

$k$ must vary inversely with stretch.