What would be the period of the free oscillations of the system shown here if mass M 1 is pulled down a little force constant of the spring is k, mass of fixed pulley is negligible and movable pulley is smooth
Text Solution
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Sol. Let the system spring extended by 
at equilibrium position. Then in this position the tension of mass
is 
and mass 
(pulley) be 
.
So, we have force equation as for the both masses-
For 
And for 
Now consider displacement of mass 
displaced byx. The corresponding displacement for mass of block
is 
. And in this position tension on 
be 
and on 
be 
.
So, for 
.
For 
Multiplying equation (iii) by 2and adding it with equation (ii), we get
Putting the value of 
, we get-
Comparing this equation with 
, we get-
Angular frequency, 
We know that the time period, 
Putting the value of 
, we get-
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