Hanging SHM

Classical Mechanics Level 4

A system consisting of a rod of mass M M and length l l is pivoted at its centre P P . Two springs of spring constants k 1 k_1 and k 2 k_2 respectively are attached as shown. They are relaxed, when the rod is horizontal. What is the time period of the rod if it is given slight angular displacement.

Find 1000 T 1000T , if T T is the time period.

Details :

  • M = 10 M = 10 kg
  • k 1 = 100 k_1 = 100 N/m
  • k 2 = 200 k_2 = 200 N/m


The answer is 662.30588.

Jaikirat Sandhu by jaikirat sandhu , 22, India

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2 solutions

Ankith A Das
Mar 5, 2015

10 Helpful 0 Interesting 0 Brilliant 0 Confused
Mircea Bejan
Jan 18, 2016

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Solid, standard solution. I would recommend attempting this with the Lagrangian approach, and exploring the coupling of more rods (i.e. a chain of hinged rods, with springs at each junction).

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