It　is　indicated　from　the　finite　duration　instance　that　time　delay　is　possible　in　structural　maximum　displacement.　Structural　natural　period　is　closely　connected　with　the　time　of　maximum　displacement.　Especially,　in　long　period　structures,　displacement　is　mainly　controlled　by　transient　vibration.　In　this　paper,　the　earthquake　transient　responses　are　got　by　wavelet　transform,　amplitude　adjustment　and　linear　superposition.　It　is　approved　that　besides　the　sympathetic　vibration,　the　maximum　displacement　of　a　long　period　structure　could　occur　in　the　case　that　external　loads　stop　but　structural　transient　vibration　still　has　great　amplitude.　Furthermore,　for　long　period　structures,　there　is　close　relationship　between　the　transient　vibration　and　the　duration.