Question

Two blocks (m = 5.00 kg and M = 11.0 kg) and a spring (k = 250.0 N/m) are arranged on a horizontal, frictionless surface. The coefficient of static friction between the two blocks is 0.400. What is the maximum possible amplitude of simple harmonic motion of the system if no slippage is to occur between the blocks? horizontal oscillations static friction no friction

Answer 1

when the blocks are arranged as shown in the diagram, there will be pseudo acceleration acting on the mass m and thus pseudo force will be acting on it. when this pseudo force becomes equal to the frictional force between the blocks, than the maximum limit is reaches. Untill than both the blocks will move with same acceleration.

Let the amplitude be x.

Toma . Let maximum pseudo acceleration be kx = (M+ m)a force balance. hence ar ka (M +m Bolancing forces on om we get, f-ma= 0 i.e. No motion. na = mkx (Mtm). f = 4N- og ung og ug = kx Mtm) x= (M+ m) ug (5+11) o x 10 250 2 = 0.256 m.