First slide

Applications of SHM

Question

If a spring of force constant 'K' is cut into three equal parts then the force constant of each part will be

Moderate

A

$\frac{K}{3}$
B

$K$
C

$3 K$
D

$6 K$

Solution

$F o r c e e q u a t i o n f o r m a s s a t t a c h e d t o a s p r i n g i s F = - k x w h e r e k i s f o r c e c o n s \tan t a n d x i s d i s p l a c e m e n t o f t h e m a s s$
$f o r a l e n g t h l o f s p r i n g e q u a t i o n o f f o r c e i s F = - k l - - - (1) w h e n t h e s p r i n g i s c u t i n t o 3 e q u a l p a r t s e q u a t i o n o f f o r c e i s F = - k^{1} \frac{l}{3} - - - (2) s u b s t i t u t e (1) i n (2) - k l = - k^{1} \frac{l}{3} \Rightarrow k^{1} = 3 k a l t e r n a t e s o l u t i o n : * * * * * F = - k x \Rightarrow k_{1} l_{1} = k_{2} l_{2} k l = k_{2} \frac{l}{3} s o k_{2} = 3 k$

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