Question

Find the steady ferce which is a Square wave of amp litude A ard penod T state respanse of an undampecl mass-Spring system to Fot) 14

Answer 1

Write the expression for the square wave 1 Sin L -13.5.2 ntt F(t) 2T Write the expression for the Equation of motion of undamped spring mass system mx+loc-F(t) 0 (1) Write the steady state response of the system

4 = A- L-13.5 1 ntt -Sin 2T 4 nnt nt x A-x == -COs 2T 2-13,5 2T 4 4 8n 1 nnt -COs 2T T -13.5 4 16n2T A ntt -CoS 2T -13.5 16n A- nt and Substitute for COS 2T -13.5 4 1 nnt for x in Equation (1) 2T A- -S1n L 13.5. 4 Il

16n'r mA T2 4 kA nnt nnt - F (t) 2T -sin -13.5 2 -coS 2T -135 4 4 Thus the steady is state response 16n m A T2 4 +kA- nt F (t)-0 -COS -$in 2T 2T T 13,5. 4 4