MT-1620 al.2002 shift the time{=0@t=τ→(t-t use t=T m g(t τ)=0 Thus q()=C sino(t-1)+C2 coso( Initial Conditions give 0→C,=0 t=T m n10 Thus: q(t) sin o(t h10 With Paul A Lagace @2001 Unit 20-14qt qt MIT - 16.20 Fall, 2002 • shift the time {t’ = 0 @ t = τ ⇒ (t - τ)} • use: 1 qt ˙ ( = τ ) = m qt ( = τ ) = 0 Thus: () = C1 sinω (t − τ ) + C2 cosω (t − τ ) Initial Conditions give: qt ( = τ ) = 0 ⇒ C2 = 0 1 1 1 qt = τ ) = ⇒ = C1ω ⇒ C1 = m ω ˙ ( m m Thus: 1 () = sin ω (t − τ ) m ω with: ω = k m Paul A. Lagace © 2001 Unit 20 - 14