Q- A harmonic force F_{0 }sin(ωt) is applied to mass m_{1} which in turn is coupled to springs of spring constants k_{1, }k_{2} and k_{3}. Let x_{1} and x_{2 }be the deviations from equilibrium for m_{1 }and m_{2}, respectively. The blocks moves on a horizontal frictionless table.

(a) Write the equations of motion for the two blocks. Use x_{1} and x_{2} as your variables.

(b) Find the normal frequencies of the system, that is, when the external force is absent. Assume for this part and the remainder of the problem the springs are the same and the masses are equal.

(c) Solve for the steady state motion with the force, that is find x_{1} and x_{2} as functions of time.