Calculate the response of a clamped-free bar to an initial

Question

Calculate the response of a clamped-free bar to an initial displacement of 1 cm at the free end and a zero initial velocity.

Assume that ρ = 7.8 x 10³ kg/m₃ , a = 0.001 m₂ , E = 10¹⁰ N/m₂ , and l = 0.5 m. Plot the response at x = l and x = l/2 using the first three modes.