Question 109: Oscillations

Question

If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor :

Accepted Answer

$${1 \over {{K_{eq}}}} = {1 \over {{K_1}}} + {1 \over {{K_1}}}$$
$$ \Rightarrow {K_{eq}} = {{{K_1} 	imes {K_1}} \over {{K_1} + {K_2}}} = {{K_1^2} \over {2{K_1}}} = {{{K_2}} \over 2}$$
$$ 	herefore $$ $$T' = 2\pi {\sqrt {{m \over {{K_{eq}}}}} } $$
$$ = 2\pi {\sqrt {{m \over {{{{K_1}} \over 2}}}} } $$
$$ = 2\pi {\sqrt {{{2m} \over {{K_1}}}} } $$
$$ = \sqrt 2 T$$ [ where $$T = 2\pi {\sqrt {{m \over {{K_1}}}} } $$]

Answer

$${1 \over 2},2\sqrt 2 $$

Answer

$${1 \over 4},2\sqrt 2 $$

Answer

$${1 \over 2},\sqrt 2 $$

Answer

$${1 \over 4},\sqrt 2 $$

Oscillations

If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor :

Choose the correct answer: