Question

A block $A$ is connected to spring and performs simple harmonic motion with a time period of 2 s. Another block $B$ rests on $A$. The coefficient of static friction between $A$ and $B$ is ${\mu }_s=0.6$. The maximum amplitude of oscillation which the system can have so that there is no relative motion between $A$ and $B$ is (take ${\pi }^2=g=10$)

• A. 0.3 m
• B. 0.6 m
• C. 0.4 m
• D. 0.5 m

Answer 1

The correct option is B 0.6 m


Let A be the maximum amplitude of oscillation for the required situation. Then $f=m{\omega }^{2}x$ (from free body diagram of blocks)
For required condition $f=m{\omega }^{2}A$
i.e., $m{\omega }^2{\mu }_{S}mg$
$⟹A<\frac{0.6\times g}{\frac{4p{i}^2}{4}}=0.6⟹A_{max}=0.6m$