Physics
Physics
3rd Edition
ISBN: 9781259233616
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 10, Problem 46P
To determine

The frequency of oscillation of the spring without anybody sitting on the wooden horse.

Expert Solution & Answer
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Answer to Problem 46P

The frequency of oscillation of the spring without the child is 2.5Hz.

Explanation of Solution

The mass of the child is 24kg, the compression of the spring is 28cm and the frequency of oscillation with the child sitting on the horse is 0.88Hz.

Physics, Chapter 10, Problem 46P

Write the expression for total force in vertical y-direction on the spring when the child is at equilibrium position. (Refer figure 1)

Fy=0kymg=0     

Here, k is the spring constant, m is the mass of the child, y is the compressed distance of the spring and g is the acceleration due to gravity.

Rearranging the above equation for k

k=mgy                                                                          (I)

Write the expression for the frequency when there’s nobody on the horse

fh=12πkmh                                                                           (II)

Here, fh is the frequency of the spring without the child and mh is the mass of the horse.

Write the expression for force constant of the spring

k=mωc2=(mc+mh)ωc2

Here, m is the total mass on the spring, mc is the mass of the child and ωc is the angular frequency of the spring with the child.

Rearranging the above equation for mh

mh=kωc2mc                                                                          (III)

Substitute (III) in (II)

fh=12πkk/ωc2mc                                                                            (IV)

Substitute 24kg for m, 9.80ms2 for g and 28cm for y in (I) to find k.

k=(24kg)(9.80ms2)28 cm=(24kg)(9.80ms2)28×102 m=840Nm1

Substitute 840Nm1 for k and 0.88Hz for ωc and 24kg for mc in (IV) to find fh

fh=12π840Nm1(840Nm1/(0.88Hz)2)24kg=12π840Nm1(840kgms2m1/(0.88Hz×2π rads1)2)24kg=2.5Hz

Thus, the frequency of oscillation of the spring without the child is 2.5Hz.

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Chapter 10 Solutions

Physics

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