Randall D. Knight — Oscillations: Problem 80

The Timoshenko oscillator is an ingenious device to measure coefficients of kinetic friction. FIGURE CP15.80 shows a plate of mass \(m\) supported by two rollers a distance \(L\) apart. The rollers spin at a high speed in opposite directions, as shown, so that they are slipping against the bottom of the plate with coefficient of kinetic friction \(\mu_k\). Let \(x\) measure the position of the plate’s center of mass relative to the midpoint between the rollers. Newton’s second law for the plate leads to a SHM equation for \(x\) and predicts the oscillation frequency in terms of \(m\), \(L\), and \(\mu_k\). Suppose a 250 g plate oscillates with a 1.5 s period on two spinning rollers 12 cm apart. What is the coefficient of kinetic friction between the plate and the rollers?