Q.81

Expert-verifiedFound in: Page 419

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

shows a uniform rod pivoted at one end. The other end is attached to a horizontal spring. The spring is neither stretched nor compressed when the rod hangs straight down. What is the rod’s oscillation period? You can assume that the rod’s angle from vertical is always small.

The rod's oscillation period is about

mass of the rod

length of the rod

spring constant

acceleration due to gravity

Considering the complete pendulum to be having a smaller angle of inclination,

The torque imposed by the spring

The torque from gravitational force

Therefore the net torque

Recalling Newton's second law for rotational motion

Comparing with linear acceleration

since and

so

since the moment of inertia of a solid thin rod pivoting about its edge is , therefore the equation for the time period becomes:

Plugging all the values, we get

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