Explanation Write the expression for time period for simple pendulum. T simple = 2 π l g (I) Here, T simple is the time period for simple pendulum, g is the gravitational acceleration, l is the length of the pendulum. Write the expression for the time period for a physical pendulum. T physical = 2 π I m g h (II) Here, T physical is the time period, g is the gravitational acceleration, h is the length from the center to axis of rotation, m is the mass and I is the moment of inertia. Write the expression for moment of inertia from parallel axis theorem. I = 1 12 m l 2 + m h 2 (III) Here, l is the length of the pendulum. Write the expression for the length. l = x + y (IV) Here, x , y are the distances. Write the expression for the length from the center to axis of rotation. h = ( x − y / 2 ) (V) Rewrite the expression (II) by using (III), (IV) and (V). T physical = 2 π 1 12 m ( x + y ) 2 + m ( x − y / 2 ) 2 m g ( x − y / 2 ) = 2 π 1 12 ( x + y ) 2 + ( x − y / 2 ) 2 g ( x − y / 2 ) (VI) Write the expression for the error. r = [ T simple − T physical T simple ] × 100 % (VII) Here, r is the error. Conclusion: Substitute, 80 cm for l , 9.8 m/s 2 for g in equation (I) to find T simple . T simple = 2 π [ ( 80 cm ) ( 1 × 10 − 2 m 1 cm ) ] ( 9

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Chapter 13, Problem 41P

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The time period for simple pendulum and physical pendulum and the error in the simple pendulum approximation.

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Chapter 13, Problem 40P

Chapter 13, Problem 42P

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