Concept explainers
(a)
The time period of oscillating system.
(a)
Explanation of Solution
Introduction:
Time period of oscillating system is the time required by system to complete one oscillation.
The free body diagram of system is drawn below.
Here,
Write the expression for time period of the pendulum.
Here,
Write the expression for resultant force in horizontal direction.
Substitute
Here,
Write the expression for resultant force in horizontal direction.
Substitute
Here,
Rearrange the above expression in term of
Substitute
Substitute
Rearrange the above expression in term of
Compare the above expression with the equation of differential equation of S.H.M.
The value of angular frequency is
Substitute
Conclusion:
Thus, the time period of oscillating system is
(b)
The value of force constant.
(b)
Explanation of Solution
Given:
The mass of bob is
The first time period of the pendulum is
The second time period of the pendulum is
Formula:
The free body diagram of system is drawn below.
Here,
Write the expression for time period of the pendulum.
Here,
Write the expression for resultant force in horizontal direction.
Substitute
Here,
Write the expression for resultant force in horizontal direction.
Substitute
Here,
Rearrange the above expression in term of
Substitute
Substitute
Rearrange the above expression in term of
Compare the above expression with the equation of differential equation of S.H.M.
The value of angular frequency is
Substitute
Calculation:
For
Substitute
For
Substitute
Conclusion:
Thus, the value of force constant is
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Chapter 14 Solutions
Physics for Scientists and Engineers
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