Question

Suppose that one oscillation of a swinging lamp takes 5.5s. What maximum speed does the lamp have if its maximum angle from vertical is 3.0degrees?

I first found L to be 7.51m. That was right.

Now, I calculated the angular frequency of the pendulum to be 1.14.

I'm pretty sure you have to multiply the angular frequency by the maximum angle. So I'm getting 3.427. Is that right or wrong?

Answer 1

If the period is 5.5 s,
2 pi sqrt (L/g) = 5.5 s
L/g = 0.766 L = 7.51 m

Elevation change during swing = H
(1 = cos 3)* L = 0.0103 m

Maximum speed is
M g H = (1/2) M V^2
V^2 = 2gH = 0.20 m^2/s^2
V = 0.45 m/s