A large block P attached to a light spring executes horizontal, simple harmonic

Question

A large block P attached to a light spring executes horizontal, simple harmonic motion as it slides across a frictionless surface with a frequency f. Block B rests on it as shown in the following figure, and the coefficient of static friction between the two is ?s. What maximum amplitude of oscillation can the system have if block B is not to slip? (Use any variable or symbol stated above along with the following as necessary: ? and g.)

Explanation / Answer

i assume that block P was attached to a spring to have a simple harmonic motion. Lets M be the mass of both block P&B ----> f = 1/(2pi) * sqrt(k/M) ----> k = 4*pi^2*f^2*M Now, first consider the block B: Newton's 2nd law: f(static) = m(B)* a f(static) m(B)*g*u = m(B)*a(max) , m(B) will be canceled out ----> a(max) = g*u 2nd, consider system of block P and block B with total mass of M: F(spring) = M*a k*x = M*a k*x(max) = M*a(max) 4*pi^2*f^2*M*x(max) = M*g*u , M will be canceled out ----> x(max) = g*u/(4*pi^2*f^2) = 9.8*0.6/(4*3.14^2*1.5^2) = 0.0662 m

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