MT-1620 al.2002 m t+E T+E a unit impulse at time t is thus a free vibration problem with an initial velocity(equal in magnitude to the inverse of the mass) Note: Units are consistent since the integral of 8(t-t)is a force x time. so length mass x ox time Force x time (time dt mass mass length city veloci t ime So use the homogeneous solution qt)=csinot C2cosat but Paul A Lagace @2001 Unit 20-13qt MIT - 16.20 Fall, 2002 dq dt m    = τ ε + 1 ( ) q = τ ε + 0 A unit impulse at time τ is thus a free vibration problem with an initial velocity (equal in magnitude to the inverse of the mass) Note: Units are consistent since the integral of δ(t - τ) is a force x time. So: mass × length2 × time dq  Force × time (time) = =  dt  mass mass = length = [velocity] time So use the homogeneous solution: () = C1 sinω t + C2 cosω t but: Paul A. Lagace © 2001 Unit 20 - 13