In case of linear vibration 'Time period' or 'Frequency' will be same for different displacement ?

[malam]

I need help from this community.

[VladimirN]

Could you describe the initial problem in more detail?

[Fred_Kohlhepp]

For a basic oscillator, you are correct:

[malam]

Dear Sir,

I have no idea about basic Oscilator. Please give me some knowledge about it. I am working in' Functionally graded beam'.

Is it a basic oscilator ?

[Fred_Kohlhepp]

A "basic oscillator" has two requirements:

1. The spring is a "perfect" spring--the spring force is proportional to deflection over the range of motion
2. There is no damping.

From what (little) I've read about "functionally graded beams,"  it seems likely that one or both of these assumptions will not be valid.

As several other posts have stated, if you want better answers, give us more information about your problem.  (An attached Mathcad calculation sheet [use  the advanced editor] is always a good incentive.)

[RichardJ]

The frequency and displacement of a vibration are independent. For a given frequency a larger displacement means a larger acceleration.

If that doesn't answer your question, then please post a more detailed question.