In this article, we will list the motion and frequency equations for important vibratory systems asked in GATE Mechanical Engineering and other UPSC competetive exams. 

1) Spring mass system:

Equation of motion: 

Frequency equation: 

(a) neglecting spring mass, 

(b) considering spring mass, 

2) Bifilar suspension:

Equation of motion: 

Frequency equation: 

3) Trifilar suspension:

Equation of motion: 

Frequency motion: 

4) Simply supported beam carrying central load:

Equation of motion: 

Frequency equation: 

5) Simply supported beam carrying UDL:

Equation of motion: 

Frequency equation: 

6) Fixed beam carrying central load:

Equation of motion: 

Frequency equation: 

7) Spring mass pulley system:

Equation of motion: 

Frequency equation: 

8) Simple pendulum with rod mass:

Equation of motion: 

Frequency equation: 

9) Compound pendulum:

Equation of motion: 

Frequency equation: 

10) Conical pendulum:

Equation of motion: 

Frequency equation: 

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Mechanical Engineer

The radius of gyration of a compound pendulum about the point of suspension is 100 mm. The distance between the
point of suspension and the centre of mass is 250 mm. Considering the acceleration due to gravity as 9.81 m/s2. The
natural frequency (in radian’s) of the compound pendulum is ____________

This is GATE 2017 Set 2 question based on compound pendulum. If we use this formula given in the list for compound pendulum, obtained answer is not correct. Kindly help Sir.

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These are helpful. Thanks.

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