Concept explainers
A 6-kg uniform cylinder can roll without sliding on a horizontal surface and is attached by a pin at point C to the 4-kg horizontal bar AB. The bar is attached to two springs, each having a constant of
(a)
The period of vibration of the given system.
Answer to Problem 19.39P
Period of vibration,
Explanation of Solution
Given information:
Mass of cylinder
Mass of bar
Amplitude
Spring constant
Firstly we draw the free body diagram of the bar and the cylinder separately and calculate forces acting upon them. For the bar;
But,
Then,
Now, for the disc,
Now, moment of inertia at point C,
Put the values of equation (1) and (3) in equation (2);
Here,
Compare the above equation with un-damped equation of vibration;
Thus, the time period:
(b)
The maximum velocity of bar AB.
Answer to Problem 19.39P
Velocity,
Explanation of Solution
Given information:
Mass of cylinder
Mass of bar
Amplitude
Spring constant
Firstly, we draw the free body diagram of the bar and the cylinder separately and calculate forces acting upon them. For the bar;
But,
Then,
Now, for the disc,
Now, moment of inertia at point C,
Put the values of equation (1) and (3) in equation (2);
Here,
Compare the above equation with un-damped equation of vibration;
Now, maximum velocity:
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