Question

A uniform spring has certain mass suspended from it and it's period of vertical oscillations is t1. The spring is now cut in 2 parts having lengths in ratio 1:2

Answer 1

Hello buddy,

I assume you're asking new time period wrt older one.

◆ Answer-

T' = 0.4714 T

◆ Explaination-

Let k be initial force constant of spring, k1 and k2 be force constant of new springs.

We can derive,

l1/l2 = 2 => x1/x2 => 2 => k1/k2 = 1/2 ...(1)

As initially these lengths were in series-

1/k = 1/k1 + 1/k2

1/k = 1/k1 + 1/2k1

Solving this,

k1 = 3k/2

k2 = 3k

When these two strings are connected in parallel,

k' = k1 + k2

k' = 3k/2 + 3k

k' = 9k/2

Time period is

T'/T = √(k/k')

T'/T = √(2/9)

T' = 0.4714 T

Hope this helps...