A rod of mass m and length L is hinged at its one end and carries a block of same mass m at its lower end. Two springs of same force constant k are installed at distances a = L /2 and b = L /4 respect

Question

A rod of mass m and length L is hinged at its one end and carries a block of same mass $m$ at its lower end. Two springs of same force constant k are installed at distances $a = L /2$ and $b = L /4$ respectively as shown in the figure. If the whole arrangement lies in the vertical plane, the frequency of small vibration is :

TestHub · Accepted Answer

mgL sin θ + mg 2 L ​ sin θ + k ( b θ ) b + k ( a θ ) a = 3 4 mL 2 ​ α α 3 4 mL 2 ​ = ( 3 mg 2 L ​ + 16 k 5 L 2 ​ ) θ f = 2 π 1 ​ 3 4 mL 2 ​ 2 3 mgL ​ + 16 ksL 2 ​ ​ ​

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