MT-1620 Fall 2002 from mathematics know this is (0)=C sinat C cost general solution Now use the initial conditions 0q=9→C q g0 This results in g(t)= q sinat go cost ith This is the basic, unforced response of the system So if one gives the system an initial displacement a and then lets go Paul A Lagace @2001 Unit 20-4qt MIT - 16.20 Fall, 2002 from mathematics, know this is: q t() = C1 ′sinω t + C2 ′ cosω t general solution Now use the Initial Conditions: @ t = 0 q = q0 ⇒ C2 ′ = q0 @ t = 0 q˙ = q˙0 ⇒ C1 ′ = q ˙ 0 ω This results in: () = q ˙ 0 sinω t + q0 cosω t ω with: ω = k m This is the basic, unforced response of the system So if one gives the system an initial displacement A and then lets go: q0 = A q ˙ 0 = 0 Paul A. Lagace © 2001 Unit 20 - 4