A bob of simple pendulam of mass 2kg is oscillating such that at the mean position its velocity is 5m/s .Calculate the height of bob at extreme position
Answers
At what positions does the pendulum have the maximum and minimum velocity?
OP: At what positions does the pendulum have maximum and minimum velocity?
A pendulum swings from the mean position to extreme position on one side, back to the mean position, going to the extreme position on the other side, back to the mean position. This constitute one complete vibration or oscillation.
The velocity of the Pedulum varies in its oscillation. The velocity of the particle when it is moving from the mean position say to the right, changes from a velocity to the right, at the extreme position to a velocity to the right. In the change of direction of the velocity from say a positive to a neagative, it needs to passe through zero. So velocity is zero at the extreme. Same thing happens at the other extreme. There the velocity changes from a velocity to the left to a velocity to the right. And at that extreme position the velocity is zero.
So velocity is zero and minimum at the two extremes.
The veocity of the pendulum is maximum when it is passing through the mean position.
We could understand this in terms of coservation of energy. At the mean position, the Bob is at the least height. When you move the Bob to the extreme, say on the right, the Bob is at a slightly raised height compared to the mean position. All its energy is potential energy. Since kinetic energy is zero, velocity is zero at extremes. At mean position the energy is all kinetic energy, so its velocity needs to be maximum.
It is due to the fact that the velocity at the mean position is maximum, that oscillations are counted when the Bob of the Pedulum passes the mean position successively. Since the velocity is maximum, the mean position, is more sharply defined, and determining the time period by counting the oscillations completed by Bob passing through the mean position is more accurate.
In physics practicals, doing the experiments is only one part, but a bigger part is, why do we do the way we do. One of the question in viva- voce could be, “ Why should we count the oscillations of the pendulum, by counting the passage of the Bob through the mean position, rather than the extreme points”?
The answer is that the mean position of oscillations is sharply defined as the velocity of the Bob is maximum when the Bob is in this position. Counting from extreme positions has two drawbacks. First at the extreme positions)points, the velocity is zero and so these are less sharply defined points, second the amplitude keeps decreasing, making the extreme positions still more uncertain.