Question

two identical springs of constant K are connected,first in series &then in parallel. A metal block of mass m is suspended from their combination. the frequency of vertical oscillation will be in a ratio________________.
a)1:4
b)1:2
c)2:2
d)4:1​

Answer 1

▶ Solution :

Given :

▪ Two identical springs of constant K are connected first in series and then in parallel.

▪ A metal block of mass m is suspended from their combination.

To Find :

▪ The ratio of frequencies of vertical oscillation.

Concept :

✏ Formula of equivalent spring constant for series connection is given by

$\boxed{\bf{\pink{K_{eq}=\dfrac{K_1K_2}{K_1+K_2}}}}$

✏ Formula of equivalent spring constant for parallel connection is given by

$\boxed{\bf{\orange{K_{eq}=K_1+K_2}}}$

✏ Formula of frequency in terms of mass of object and equivalent spring constant is given by...

$\boxed{\bf{\green{f=\dfrac{1}{2\pi}\sqrt{\dfrac{K_{eq}}{M}}}}}$

Calculation :

✏ Here mass is constant, so we can say that

$\implies\sf\:f\propto\sqrt{{K_{eq}}}\\ \\ \implies\sf\dfrac{f_1}{f_2}=\sqrt{\dfrac{K_s}{K_p}}\\ \\ \implies\sf\dfrac{f_1}{f_2}=\sqrt{\dfrac{1}{4}}\\ \\ \implies\boxed{\bf{\purple{f_1:f_2=1:2}}}$

Answer 2

Explanation:

n1:n2=1:2

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