Problem 3 (5 points) Define the convolution integrals to calculate the response of a 1-DOF spring-mass-damper system excited by an arbitrary input force F(t), as shown in the figure below. The system can be described by an equation of motion m(t) + cx(t) + kx = F(t). Use fi(t), fz(t), fz(t) to represent the three parts of the forcing function F(t) to derive your convolution expression. Define new variables or functions if necessary. F(t) fu(t) f3(t) f0 t Problem 3 (5 points) Define the convolution integrals to calculate the response of a 1-DOF spring-mass-damper system excited by an arbitrary input force F(t), as shown in the figure below. The system can be described by an equation of motion m(t) + cx(t) + kx = F(t). Use fi(t), fz(t), fz(t) to represent the three parts of the forcing function F(t) to derive your convolution expression. Define new variables or functions if necessary. F(t) fu(t) f3(t) f0 t