Find the blanks:

Explanation

a. For small amplitude the tow blocks oscillate together. The angular frequency is
`omega=sqrt(k/(M+m))`
and so the time period `T=2pisqrt((M+m)/k)`.
b. The acceleration of the blocks at displacement x from the mean position is
`a=-omega^2x=(-kx)/(M+m)` ltbr. the resultant force on teh upper block is therefore
`ma=(-mkx)/(M+m)`
this force is provided by friction of the lower block. Hence the magnitude of the frictioN/Al force is `(mk|x|)/(M+m)`
c. Maximum force of friction required for simple harmonic motion of the upper block is `(mkA)/(M+m)` at the extreme positions. But the madximum frictioN/Al force can only be `mumg`. Hence
`(mkA)/(M+m)=mumg or A=(mu(M+m)g)/k`.