Question

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?

Answer 1

k2 and m1 will give the greatest period of oscillation.

Step-by-step explanation:

Given:

Two springs with spring constant
`k_1,k_2` and
`k_1>k_2` .

Mass attached with springs are
`m_1,m_2` also
`m_1>m_2` .

We have to find period of oscillation:

Formula:

⇒
`T=2\pi \sqrt{(m)/(k) }` ...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
`k_2` .

And the mass to be paired is the greater mass that is
`m_2` .

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