Engineering
Physics
Basics of Simple Harmonic Motion
Stress Strain and Hookes Law New
Question

A highly rigid cubical block A of small mass M and side L is fixed rigidly on to another cubical block of same dimensions and of low modulus of rigidity η such that the lower face of A completely covers the upper face B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side face of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by :

2πMηL 

2πL 

2πMLη 

2πM 

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Solution
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Modulus of rigidity η=F 

We know, A = L2 
For small θ, 
θ=xL 
Restoring force F = –ηAB
                  F = –ηLx
Acceleration, a=Fm=ηLMx   equation(1)
∵   a ∝ (–x)
∴  Time period, T=2πxa 
T=2πM¯ηL