Flag Wave Motion> A wheel is free to rotate about its fixed...
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A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes a distance r from the axle, as shown in Fig. 17-38. Assuming that the wheel is a hoop of mass M and radius R, obtain the angular frequency of small oscillations of this system in terms of M, R, r, and the force constant k. Discuss the special cases r = R and r = 0.
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

Hrishant Goswami , 10 Years ago
Grade 10
anser 1 Answers
Navjyot Kalra

Last Activity: 10 Years ago

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