(a)
The natural frequency
(a)
Answer to Problem 3.1P
The natural frequency
Explanation of Solution
Write the formula to find the natural frequency
Here,
Write the formula to find the period
Here,
Conclusion:
Substitute
Thus, the natural frequency is
Substitute
Thus, the period is
(b)
The total energy.
(b)
Answer to Problem 3.1P
The total energy is
Explanation of Solution
Write the formula to find the energy
Here,
Conclusion:
Substitute
Thus, the total energy is
(c)
The maximum speed.
(c)
Answer to Problem 3.1P
The maximum speed is
Explanation of Solution
The maximum velocity of the system is attained when the total energy of the system is equal to the kinetic energy of the system.
Write the formula to find the kinetic energy
Here,
Conclusion:
Substitute
Thus, the maximum velocity is
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Chapter 3 Solutions
Classical Dynamics of Particles and Systems
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