A spring of force constant k is cut into two parts whose lengths are in the ratio 1:2. The two parts are now connected in the parallel and
a block of mass M is suspended at the end of the combined spring. The time period of oscillation of the block is?

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Solution

Ratio of spring constants of the two spring segments = 2:1 (larger segment will have smaller spring constant)

So consider the values to be 2x and x. When these two are in series, they give rise to the original spring. So

2x * x / (2x + x) = k

which gives x = 3k/2.

So spring constants are 3k/2 and 3k.

When they are in parallel, effective spring constant = 3k + 3k/2 = 9k/2

Time period T = 2*pi sqrt (2m/9k)

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A spring of force constant k is cut into two parts whose lengths are in the ratio 1:2. The two parts are now connected in the parallel and a block of mass M is suspended at the end of the combined spring. The time period of oscillation of the block is?

A spring of force constant k is cut into two parts whose lengths are in the ratio 1:2. The two parts are now connected in the parallel and
a block of mass M is suspended at the end of the combined spring. The time period of oscillation of the block is?