Question

You are designing a pendulum clock to have a period of 1.0 s. The acceleration of gravity is 9.81 m/s2 . How long should the pendulum be? Answer in units of m.

Answer 1

.248490m

Step-by-step explanation:

Using the equation:

T=Time

L=Length

g=Gravitational Force≈9.81

T=
`2\pi √(L/g)` or easier written to find the length using time:
`L=(T^(2) *g)/(4\pi^(2) )`

so simply plugging in 1 for T we get
`(9.81)/(4\pi^(2) ) \\`≈.25m

Answer 2

0.25 m

Step-by-step explanation:

The period of a pendulum is given by

`T=2 \pi \sqrt{(L)/(g)}`

where in this case

T = 1.0 s is the period of the pendulum

g = 9.81 m/s^2 is the acceleration due to gravity

L is the length of the pendulum

Re-arranging the equation and solivng for L, we find the length of the pendulum:

`L=g ((T)/(2 \pi))^2=(9.81 m/s^2)((1.0 s)/(2\pi))^2=0.25 m`