find the acceleration of gravity for a pendulum that oscillates 1.5 times every 18 seconds and has a length of 3.54m

Fundamental equation for SHM:   w = (k/m)^1/2  where w is angular frequency

Or since P = 1 / f = 2 pi / w = 2 pi (m / k)^1/2

The equivalent equation for a simple pendulum is:

P = 2 pi (L / g)^1/2    or g = 4 pi^2 L / P^2

g = 4 pi^2 * 3.54 / 12^2 = .971 m / s^2

Something wrong - should be 9.71 m / s^2

c. magnitude and direction

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s