Engineering
Physics
Newtons Second Law of Motion
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 onto another cubical block B of same dimensions and of low modulus of rigidly η such that lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force is applied perpendicular to one the side face of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by

2πMηL

2πMηL

2πMLη

MLη

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Solution
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Modulus of rigidity, η=F

Here, A = L2 and θ=xL
Therefore, restoring force is,
 
F = –ηAθ = –ηLx
or
Acceleration, a=FM=ηLMx
Since, a ∝ –x, oscillations are simple harmonic in nature, time period of which is given by,
T=2πDisplacementAcceleration=2πxa
=2πMηL