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Oscillation find frequency of small oscillation of a thin uniform vertical rod of mass M and length L when its upper end is hinged and lower end attached to a spring of stiffness K on either side of the rod,the free end of each spring connected to wall.

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Does this help, it may be a start.
A Cos[w t - è[t]] + B è''[t]==0, where A and B are arbitrary constants?

If you expand the Cosine term, you get A Cos[w t] Cos[è[t]] + A Sin[w t] Sin[è[t]] +B è''[t] ==0, which can be approximated as:

B è''[t] + A Sin[w t] è[t]== -A Cos[w t]

So is the frequency of small oscillations just Sqrt[(A Sin[w t])/B]?

Posted on Nov 07, 2007

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GM Full-Size Trucks 1988-1998 Repair Information Doors - REMOVAL & INSTALLATION

R/V Series
See Figures 1, 2 and 3
If the door being removed is to be reinstalled, matchmark the hinge position.
  1. If the door is to be replaced with a new one, remove the trim panels weathersheets and all molding.
efc6815.jpg

Fig. 1: Door hinge-R/V Series
  1. If the door is to be replaced with a new one, remove the glass, locks and latches.
  2. If equipped with a wiring harness, remove the trim panel and disconnect the harness. Guide the wiring out of the door.
  3. Support the door and remove the hinge-to-body attaching bolts. Lift the door from the truck.
  4. Install the door.
  5. Perform the alignment procedures indicated below.

3a1bddd.jpg

Fig. 2: Door hinge components-C/K Series

4ab81ea.jpg

Fig. 3: Removing the hinge spring


C/K Series
  1. On trucks with power components in the door, disconnect the battery ground cable.
  2. On trucks with power components in the door, remove the cowl side vent cover.
  3. On trucks with power components in the door, disconnect the wiring going to the door, under the dash panel. Feed the wiring through the door pillar.
  4. Cover the door hinge spring with a heavy towel. Using tool J-36604 or its equivalent, insert the blades of the tool between the spring coils and turn the barrel nut to compress and hold the spring. Remove the spring using the tool.
  5. Remove the lower hinge pin retainer.
  6. Using a plastic or rubber mallet and locking pliers, remove the lower hinge pin.
  7. Install a bolt through the lower hinges to hold the door while removing the upper hinge pin.
  8. Remove the upper hinge pin retainer.
  9. Remove the upper hinge pin.
  10. Support the door and remove the bolt from the lower hinge.

To install:
  1. Position the door and install the bolt in the lower hinge.
  2. Install the upper hinge pin. with the pointed end up.
  3. Install a new upper hinge pin retainer.
  4. Remove the bolt from the lower hinges.
  5. Install the lower hinge pin with the pointed end down.
  6. Install a new lower hinge pin retainer.
  7. Using tool J-36604, install the hinge spring.
  8. On trucks with power components in the door, connect the wiring going to the door, under the dash panel. Feed the wiring through the door pillar.
  9. On trucks with power components in the door, install the cowl side vent cover.
  10. On trucks with power components in the door, connect the battery ground cable.
ADJUSTMENTSee Figure 4 The holes for the hinges are oversized to provide for latitude in alignment. Align the door hinges first, then the striker.
C/K series utilize hinges that are welded to the door and frame. No adjustment is possible except when replacement hinges have been installed.

66b8749.jpg

Fig. 4: Door adjustment check points
  1. If a door is being installed, first mount the door and tighten the hinge bolts lightly.
If the door has not been removed, determine which hinge bolts must be loosed to effect alignment.
  1. Loosen the necessary bolts just enough to allow the door to be moved with a padded prybar.
  2. Move the door in small movements and check the fit after each movement.
Be sure that there is no binding or interference with adjacent panels.
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R/V Series:
Door edge-to-rocker panel: 6mm Door edge-to-roof panel: 5mm Door edge-to-rear pillar: 5mm Door edge-to-front pillar: 2mm
C/K Series:
Door edge-to-rocker panel: 6mm Door edge-to-roof panel: 6mm Door edge-to-rear pillar: 4mm Door edge-to-front pillar: 7mm Door front edge-to-fender: 5mm
  1. Tighten all the bolts to 26 ft. lbs. (35 Nm).

Shims may be either fabricated or purchased to install behind the hinges as an aid in alignment.

Hope this help, TY for using Fixya (remember comment and rated this). Good luck.

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