2. Motion of a Particle Connected to a Spring Consider a particle of mass m connected to a spring with a spring (elastic) constant s = k exp(-at) at time t, where k and a are both positive. Thus, the spring constant ages over time and decreases. The governing equation for the position y(t) of the particle at time t is given by, dy + sy = 0. (1) dt2 (a) Let, z = (4k/a?m)'/² exp(-at/2). Derive the governing equation for y(2).

2. Motion of a Particle Connected to a Spring Consider a particle of mass m connected to a spring with a spring (elastic) constant s = k exp(-at) at time t, where k and a are both positive. Thus, the spring constant ages over time and decreases. The governing equation for the position y(t) of the particle at time t is given by, dy + sy = 0. (1) dt2 (a) Let, z = (4k/a?m)'/² exp(-at/2). Derive the governing equation for y(2).