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Two physical pendulums perform small oscillations about the same horizontal axis with frequencies w1 and w2. Their moments of inertia relative to the given axis are equal to i1 and i2 respectively. In a state of stable equilibrium the pendulums were fastened rigidly together. What will be the frequency of small oscillations of the com-pound pendulum?

Two physical pendulums perform small oscillations about the same horizontal axis with frequencies w1 and w2. Their moments of inertia relative to the given axis are equal to i1 and i2 respectively. In a state of stable equilibrium the pendulums were fastened rigidly together. What will be the frequency of small oscillations of the com-pound pendulum?

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

consider one physical pendulum. Let distance between center of mass and axis be 'l'. Torque 't' =mlg*(theta)=i*alpha

alpha is angular accel. alpha=(w^2)*theta,w^2 = mlg/i,w1=sqrt(m1*l1*g/i1),w2=sqrt(m2*l2*g/i2)

m1*l1=g*i1*(w1^2), m2*l2=g*i2*(w2^2)

for two combined pendulums, ml=m1*l1+m2*l2

let answer be w

w^2=(g/(i1+i2))(m1*l1+m2*l2)

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