
Concept explainers
(a)
The force constant of the spring.
(a)

Answer to Problem 18P
The force constant of the spring is
Explanation of Solution
Write the expression to calculate the force constant of the spring.
Here,
Conclusion:
Substitute
Thus, the force constant of the spring is
(b)
The frequency of oscillations.
(b)

Answer to Problem 18P
The frequency of oscillations is
Explanation of Solution
Write the formula to calculate the angular frequency for the object.
Here,
Write the formula to calculate the frequency of oscillations.
Here,
Conclusion:
Substitute
Substitute
Thus, the frequency of oscillations is
(c)
The value for the maximum speed of the object.
(c)

Answer to Problem 18P
The value for the maximum speed of the object is
Explanation of Solution
Write the expression to calculate the maximum speed of the object.
Here,
Conclusion:
Substitute
Thus, the value for the maximum speed of the object is
(d)
The position at which the maximum speed occur.
(d)

Answer to Problem 18P
The position at which the maximum speed occur is
Explanation of Solution
The maximum speed of a
Thus, the position at which the maximum speed occur is
(e)
The maximum acceleration of the object.
(e)

Answer to Problem 18P
The maximum acceleration of the object is
Explanation of Solution
Write the expression to calculate the maximum acceleration of the object.
Here,
Conclusion:
Substitute
Thus, the maximum acceleration of the object is
(f)
The position at which the maximum acceleration occur.
(f)

Answer to Problem 18P
The position at which the maximum acceleration occur is
Explanation of Solution
The object attains its maximum acceleration when the direction of the object is reversed. The object reverses its direction when it is at maximum distance from the equilibrium x position.
The object reverses its direction at the maximum position of
Thus, the position at which the maximum acceleration occur is
(g)
The total energy of the oscillating system.
(g)

Answer to Problem 18P
The total energy of the oscillating system is
Explanation of Solution
Write the expression to calculate the total energy of the oscillating system.
Here,
Conclusion:
Substitute
Thus, the total energy of the oscillating system is
(h)
The speed of the object when its position is one third of maximum value.
(h)

Answer to Problem 18P
The speed of the object when its position is one third of maximum value is
Explanation of Solution
Write the expression to calculate the speed of the object at
Conclusion:
Substitute
Thus, the speed of the object when its position is one third of maximum value is
(i)
The acceleration of the object when its position is one third of maximum value.
(i)

Answer to Problem 18P
The acceleration of the object when its position is one third of maximum value is
Explanation of Solution
Write the expression to calculate the speed of the object at
Conclusion:
Substitute
Thus, the acceleration of the object when its position is one third of maximum value is
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