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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 pails are now connected in parallel and a block of mass m is suspended at the end of the combined spring. Find the period of oscillation performed by the block

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

Grade:Upto college level

3 Answers

Simran Bhatia
348 Points
7 years ago

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)

Smriti
11 Points
4 years ago
A spring when connected by mass m gives time period T if spring is cut in n equal parts and each part connected in parallel with same mass. New time period will be
Kushagra Madhukar
askIITians Faculty 629 Points
10 months ago
Dear student,
Please find the attached solution to your problem below.
 
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)
 
Thanks and regards,
Kushagra

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