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4. A stick of mass M and length L has a uniform distribution of mass. The stick is suspended vertically from a frictionless pivot at L/4 (so that 3% of the stick lies below the pivot. Initially the stick is at rest hanging vertically. The stick is displaced at a small angle from the vertical and then released from rest. a) Prove that the stick oscillates in SHM. b) Find the period of oscillation. c) How much time does it take the stick to reach equilibrium for the first time when it is released from rest? d) How fast is the bottom end of the stick moving as it swings through the lowest point?

          4. A stick of mass M and length L has a uniform distribution of mass. The stick is suspended vertically
from a frictionless pivot at L/4 (so that 3% of the stick lies below the pivot. Initially the stick is at rest
hanging vertically. The stick is displaced at a small angle from the vertical and then released from rest.
a) Prove that the stick oscillates in SHM.
b) Find the period of oscillation.
c) How much time does it take the stick to reach equilibrium for the first time when it is released from
rest?
d) How fast is the bottom end of the stick moving as it swings through the lowest point?

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4 a stick of mass m and length l has a uniform distribution of mass the stick is suspended vertically from a frictionless pivot at l4 so that 3 of the stick lies below the pivot initially th 85213

Added by Eduardo M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

11/29/2022

Step 1

The center of mass is at L/2. The distance between the pivot and the center of mass is $d = L/2 - L/4 = L/4$. The torque due to gravity is $\tau = -Mgd\sin\theta = -Mg(L/4)\sin\theta$. For small angles, $\sin\theta \approx \theta$. So, $\tau \approx Show more…

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4. A stick of mass M and length L has a uniform distribution of mass. The stick is suspended vertically from a frictionless pivot at L/4 (so that 3% of the stick lies below the pivot. Initially the stick is at rest hanging vertically. The stick is displaced at a small angle from the vertical and then released from rest. a) Prove that the stick oscillates in SHM. b) Find the period of oscillation. c) How much time does it take the stick to reach equilibrium for the first time when it is released from rest? d) How fast is the bottom end of the stick moving as it swings through the lowest point?

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