# There is friction between M and ground and $\;(\mu_{s}=0.5)\;$ . There is no friction between m and ground . Find the maximum amplitude of S.H.M with which the block m vibrates so that the block M does not move ? $\;(g=10 m/s^2)$

$(a)\;33.3\qquad(b)\;66.7\qquad(c)\;54.9\qquad(d)\;None\;of\;these$

Answer : (a) $\;33.3$
Explanation :
Let the amplitude of S.H.M be A
The spring streches maximum by 2A
$2KA=f \quad$ (f friction force )
$f=0.5 \times 40 \times 10$
$2 \times 3 \times A=0.5 \times 40 \times 10$
$A\times 2 \times 3 =5 \times 20$
$A=\large\frac{100}{3}=33.3 \;.$