You have two springs. Spring 1 has a greater spring constant than spring 2 (k1> k2). You also have two objects, mass1 has a greater mass than mass 2 (m1> m2). Which mass and spring should be paired so that the resulting system has the greatest period of oscillation?

k2 and m1 will give the greatest period of oscillation.

Explanation:

Given:

Two springs with spring constant and    .

Mass attached with springs are also .

We have to find period of oscillation:

Formula:

⇒  ...m is the mass and k is the spring constant.

Analysis:

We can see that for greater oscillation period, mass (m) should be greater as it is in direct proportion of the formula and spring constant (k) must be smaller as it is inversely proportional to the period of oscillation.

According to the question:

We have to pair mass and spring for the greatest period of oscillation.

So,

Between the two springs we will choose the spring having less spring constant values that is .

And the mass to be paired is the greater mass that is .

The resulting system which has the greatest period of oscillation will be obtained from the pair of k2 and m1.

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.