(a)
The period of vibration.
Answer to Problem 19.41P
Period of vibration,
Explanation of Solution
Given information:
Weight of rod
Weight of disc
Spring constant
Length
Radius
The free body diagram of the given bar is as follows:
Now taking moment about point B,
Here,
And also from the statics of the diagram;
Assuming small angles
First we calculate the moment of inertia for AB,
Now, for disc the moment of inertia is,
By putting all the values in the above equation we get,
Compare the above equation with un-damped equation of vibration;
Then, Natural frequency:
And, Period
(b)
Maximum velocity at point A.
Answer to Problem 19.41P
Maximum velocity,
Explanation of Solution
Given information:
Weight of rod
Weight of disc
Spring constant
Length
Radius
The free body diagram of the given bar is as follows:
Now taking moment about point B,
Here,
And also, from the statics of the diagram;
Assuming small angles
First we calculate the moment of inertia for AB,
Now, for disc the moment of inertia is,
By putting all the values in the above equation we get,
Compare the above equation with un-damped equation of vibration;
Then, Natural frequency:
Maximum velocity:
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Chapter 19 Solutions
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