Concept explainers
(a)
The angle
Answer to Problem 19.13P
Explanation of Solution
Given information:
Angle
Length of cord
The equation of a simple harmonic motion in angular displacement is given as:
The initial condition for the system is:
Now, taking derivative of equation (1) and substitute 0 for t and 0 for
Now, For a simple pendulum:
Change the length (l) into ft.
Thus,
Again amplitude
Now, put all the above obtained values in equation (1) with
Conclusion:
The value of the angle
(b)
The magnitudes of the velocity and acceleration of the bob.
Answer to Problem 19.13P
Explanation of Solution
Given information:
Angle
Length of cord
The velocity of the bob is compute by taking derivative of equation (1);
By substituting the values of
The angular velocity of pendulum is:
The acceleration of the motion is calculated by taking the derivative of equation (2),
By substituting the values of
Now, the magnitude of acceleration at both angular and tangential direction is calculated as:
Where, an = acceleration in angular direction and at = acceleration in tangential direction.
Acceleration in angular direction
From equation (3);
And, acceleration in tangential direction
Put the values of
Conclusion:
The velocity of the bob is
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Chapter 19 Solutions
Vector Mechanics For Engineers
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