Let f(x) = 2-1 on (0,1). Expand f as a Fourier sine series and write the corresponding solutions for Temperature in a semi-infinite plate with the lower boundary fixed at f. Temperature in a rectangular plate of height H with the lower boundary fixed at f. Heat flow in one dimension with initial temperature f. Particle in a box with initial condition f. A plucked string with initial shape f. A struck string with initial velocity f.