Mechanical vibrations homeworks

[leocer]

Homework Statement

what distance x from the axis of variation O should be 1 kg
slider, the system oscillations period is 0.9 s?

T=0.9 s;
the spring stiffness k=75 N/m;
slider mass m=1 kg;
beam mass m=3 kg;

Homework Equations

I$\varphi$(over letter "..")+k$\varphi$=0
$\varphi$(over letter "..")+$\omega$^2$\varphi$=0

The Attempt at a Solution

I have no solution. Please help me to find solution. Thanks.

 

[LawrenceC]

Can you write the ordinary differential equation that describes the system in terms of rotational moment of inertia, time, spring constant, and dimenions? The moment of inertia of the system will contain an unknown distance x. Once you put the ODE in correct form, you can identify the frequency of vibration. It will contain x. Then find x such that you get the period you seek.