In the overhead view of, a long uniform rod of mass m0.6 Kg is free to rotate in a horizontal planeabout a vertical axis through its center .A spring

Sinead Mcgee 2021-05-10 Answered
In the overhead view of, a long uniform rod of mass m0.6 Kg is free to rotate in a horizontal planeabout a vertical axis through its center .A spring with force constant k = 1850 N/m is connected horizontally betweenone end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the wall. What isthe period of the small oscillations thatresult when the rod is rotated slightly and released?
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Expert Answer

oppturf
Answered 2021-05-12 Author has 94 answers

In theoverhead view of , a long uniform rodof mass ( m = 0.6 Kg) is freeto rotate in a horizontal plane about avertical axis through its center.
A spring with force constant( k = 1850 N/m ) is connected horizontally between one end of the rod and a fixed wall.
When the rod is inequilibrium, it is parallel to the wall.
Let ' T ' be the time-period of the small oscillations that result when the rod is rotated slightly and released
Let rod ( length L) rotates by angle (θ)
Let 'F ' be the force applied on the rod, then spring elongated by (x)=Lθ2
Since , the moment of force (τ)=FL2
Or (τ=FL2=kLθ2L2
=kL24θ
So, the time period (T)=2πlC
where I=mL212
C=kL24
So, T=2πm3k
Here m=0.6 kg and k=1850 N/m
T=0.06533s

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