Period and speed of pendulum?

Question

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?

Answer 1

(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.