"WTW 238 – Past Papers (2015–2024) – With Annotations."
A mass m is attached to a spring with stiffness k and a damper with coefficient c. However, the mass is not constant. The mass is a small bucket of sand that leaks at a constant rate of α kg/s. The bucket starts with mass m0 at t=0 and is displaced from equilibrium and released. Assuming the leak is slow enough that the damper and spring coefficients remain constant relative to the changing mass, derive the equation of motion and solve for x(t) for the underdamped case. wtw 238 past papers
Then came 2019. Her smile faltered. The problem wasn't just solving the equation; it was interpreting a word problem about a vibrating bridge cable with a damping coefficient that changed with wind speed—a non-linear, non-homogeneous beast. She spent forty minutes on it, filling three pages with scribbles, before she finally cracked it. "WTW 238 – Past Papers (2015–2024) – With Annotations