period and speed of pendulum?

the period of motion for a pendulum is the amount of time it takes to swing from right to left and back to right again. the period is given by the equation , where t is the period and l is the length of the pendulum.a. a pendulum has a length of 2 m. what is the period of the pendulum?b. the pendulum is lifted to a height of 1.2 m. what is the maximum speed of the pendulum?c. how would the period of the pendulum be different on the moon, where the gravitational force decreases by a factor of 6?

(a)
 
t = 2*pi / omega = 2*pi / sqrt (g/l) = 2 * pi / sqrt (9.8/2) sec = 2.84 sec
 
 
(b)
 
mgh = 0.5 mv^2
 
gh = 0.5 v^2
 
v = sqrt(2gh) = sqrt (2 * 9.8 *1.2) m/s = 4.85 m/s
 
 
(c)
 
t = 2*pi / omega = 2*pi / sqrt (g/l)
 
replace g with g/6:
 
t = 2*pi / omega = 2*pi / sqrt [(g/6)/l] = 2.45 * [2*pi / sqrt (g/l)]
 
therefore, the period on the moon is 2.45 times the period on the earth.