  We compute the spectra of the Laplace-Beltrami operator, the connection
Laplacian on 1-forms and the Einstein operator on symmetric 2-tensors on the
sine-cone over a positive Einstein manifold $(M, g)$. We conclude under which
conditions on $(M,g)$, the sine-cone is dynamically stable under the singular
Ricci-de Turck flow and rigid as a singular Einstein manifold
