Question

Two balls of unequal mass are hung from two springs that are not identical. The springs stretch the same distance as the two systems reach equilibrium. Then both springs are compressed and released. Which one oscillates faster? a. Springs oscillate with the same frequency. b. The spring with the heavier ball. c. The spring with the lighter ball. d. It is impossible do determine without additional data.

Answer 1

Answer:

a. Springs oscillate with the same frequency

Explanation:

As they both are in the same height at equilibrium, so

weight of ball must be balanced with spring force, that is

k×x=mg

k= stiffness constant of spring

x=distance stretched

g= acceleration due to gravity

so,  we can write

k/m=g/x

as the g is a constant and they stretched to same distance x so the g/x term becomes constant and

$f\propto\sqrt{k/m}$

and k/m is same for both the springs so they will oscillate at the same frequency.

hence option a is correct.