Explanation Given: Mass of bob is 2.75 lb . Length of pendulum is 24 in . . Mass of collar is 3 lb . The relation of displacement is x c = δ m sin ( ω f t ) . The maximum amplitude of displacement is 0.4 in . . Frequency is 0.5 Hz . Concept used: Draw the diagram for system as shown below: As the bob has a small displacement, from the above figure, sin θ = ( x − x c ) l Here, x is the final displacement of bob after the angular displacement, x c is the displacement and l is the length of pendulum. Write the expression for the force balance in initial condition. T = m g Here, T is the tension in string, m is the mass of bob and g is the acceleration due to gravity. Write the expression for Newton’s Law of motion in x-direction. ∑ F x = m a x Substitute − T sin θ for ∑ F x and x ¨ for a x in the above expression. − T sin θ = m x ¨ ...... (1) Here, θ is the small angular displacement and x ¨ is then acceleration in x-direction. Substitute m g for T and ( x − x c ) l for sin θ in equation (1). − m g ( x − x c ) l = m x ¨ − g l ( x − x c ) = x ¨ − g x l + g x c l = x ¨ Substitute δ m sin ( ω f t ) for x c in the above expression and rearrange To determine (b) The periodic force that should be applied to the collar to maintain periodic motion.

12th Edition

ISBN: 9781260265521

Author: BEER

Publisher: MCG

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Question

Chapter 19.4, Problem 19.110P

To determine

(a)

The amplitude of the motion of bob

To determine

(b)

The periodic force that should be applied to the collar to maintain periodic motion.

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Chapter 19.4, Problem 19.109P

Chapter 19.4, Problem 19.111P

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(a) The amplitude of the motion of bob

Solution Summary: The amplitude of motion of bob is 1.034, the length of pendulum is 24, and the mass of collar is 3