Concept explainers
(a)
The mass of the object.
(a)
Explanation of Solution
Given:
The force constant is
The amplitude of the object is
The frequency of oscillation is
Formula used:
Write the expression for the angular frequency of the object.
Here,
Simplify the above equation for
Write the expression for angular frequency in terms of frequency.
Here,
Substitute
Calculation:
Substitute
Conclusion:
Thus, the mass of the object is
(b)
The amount of spring stretched from its upstretched length when the object is in equilibrium.
(b)
Explanation of Solution
Given:
The force constant is
The amplitude of the object is
The frequency of oscillation is
Formula used:
Assume
The force at the equilibrium position
Write the expression for the net force on the object at equilibrium position.
Here,
Rearrange equation (3) in terms of
Calculation:
Substitute
Conclusion:
Thus, theamount the spring is stretched from its original length when the object is in equilibrium is
(c)
The expression for the position, velocity and acceleration of the object.
(c)
Explanation of Solution
Given:
The force constant is
The amplitude of the object is
The frequency of oscillation is
Formula used:
Write the expression for the position of object as the function of time.
Here,
Differentiate the position of the particle to determine velocity.
Here,
Divide equation (6) and (5) to obtain
Substitute
Write the expression for the frequency of oscillation.
Substitute
Calculation:
Substitute
Obtain the velocity of the object.
Substitute
Differentiate equation (6) to obtain acceleration.
Here,
Conclusion:
Thus, the position of the object is
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Chapter 14 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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