2011-04-01, 04:16 AM
A pendulum swings the fastest at the bottom, since it gains the most energy at that point.
m*g*Δh = 1/2*m*v^2
If the starting height is defined at 0, the velocity when the pendulum reaches the bottom is:
v=sqrt(2*g*h)
Clearly, the largest velocity is at height h, or the bottom, because if y(t) is the height of the bottom of the pendulum at any time t, then 0<y(t)<h.
-----
Edit: I see what you're saying now. So that verifies that the form of my first solution is correct.
How about the form of the second question?
m*g*Δh = 1/2*m*v^2
If the starting height is defined at 0, the velocity when the pendulum reaches the bottom is:
v=sqrt(2*g*h)
Clearly, the largest velocity is at height h, or the bottom, because if y(t) is the height of the bottom of the pendulum at any time t, then 0<y(t)<h.
-----
Edit: I see what you're saying now. So that verifies that the form of my first solution is correct.
How about the form of the second question?