A highly rigid cubical block $$B1$$ of small mass m and side L is fixed rigidly onto another cubical block $$B2$$ of same dimensions and of low modulus of rigidity η, such that the lower face of $$B1$$ completely covers the upper face of $$B2$$. The lower face of $$B2$$ is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of $$B1$$. After force is withdrawn, block $$B1$$ executes small oscillations, the time period of which is παmηL. The value of α is $$__________$$.

Question

A highly rigid cubical block $$B1$$ of small mass m and side L is fixed rigidly onto another cubical block $$B2$$ of same dimensions and of low modulus of rigidity η, such that the lower face of $$B1$$ completely covers the upper face of $$B2$$. The lower face of $$B2$$ is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of $$B1$$. After force is withdrawn, block $$B1$$ executes small oscillations, the time period of which is παmηL. The value of α is $$__________$$.

Infinity Learn · Accepted Answer

η$$=FA$$θ Here, $$A=L2$$ and θ$$=xL$$.  Restoring force is $$F=$$−ηAθ$$=$$−ηLx Acceleration is $$a=$$−ηLmx⇒ a∝−x∴  Oscillations are simple harmonic with ω$$=$$ηLm So,  $$T=2$$πω$$=2$$$$π$$mη$$L=$$π$$4m$$ηL⇒α$$=4$$

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η=FAθ Here, A=L2 and θ=xL. Restoring force is F=−ηAθ=−ηLx Acceleration is a=−ηLmx⇒ a∝−x∴ Oscillations are simple harmonic with ω=ηLm So, T=2πω=2πmηL=π4mηL⇒α=4

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