So we want find the coefficient of friction, which comes from F = (mu)*N, where F is the force of static friction, mu is the coefficient of friction and N is the normal force of the object. We can talk about how the penny would move after this force is reached with F = ma, where a is acceleration and m is the mass of the penny. The maximum acceleration of an oscillatory motion is a = Aω², where A is the amplitude and ω is the angular frequency. To turn ω into the regular frequency we're given, we can use ω = 2πf. Using this, our max acceleration becomes a = A(2πf)², which we can put into F=ma, so it becomes F = m(4Aπ²f²), then we can set it equal to F = (mu)N, so 4Amπ²f² = (mu)N. N, the normal force, will equal the weight force of the penny (draw a free body diagram), W = mg, where m is the mass of the penny and g is the gravitational constant (9.8m/s²). So N = W = mg, so we sub mg in for N, and we get 4Amπ²f² = (mu)mg, we solve for mu, cancelling our m's (good thing too since we don't know the mass of the penny) and we get mu = 4Aπ²f²/g, then we plug stuff in (convert mm to m by multiplying by 10⁻³) mu = 4(40*10⁻³)(3.14)²(1.75)²/(9.8) = 0.49 for our coefficient of friction. Lots of equations, but I hope that made sense!