Question 590884
2. The time (in seconds) it takes a pendulum on a grandfather clock to swing back and forth once is given by T=6.28sqrt(l/32)
Where l is the length of the pendulum in feet.
2(a) Solve this equation for l.

{{{T=6.28sqrt(l/32)}}}
/6.28

{{{(T/6.28)= sqrt(l/32)}}}

square both sides

{{{(t/6.28)^2 = l/32}}}

{{{l= 32(t/6.28)^2}}}

You can simplify .

2(b) Suppose it takes 2 seconds for the pendulum to swing back and forth once.  How long is the pendulum?

{{{l= 32(t/6.28)^2}}}

plug t= 2 

{{{l= 32(2/6.28)^2}}}

l= 3.25 feet

2(c) Suppose a pendulum is 1.5 feet long.  How long will it take the pendulum to swing back and forth once?

{{{T=6.28sqrt(l/32)}}}

plug l=1.5

{{{T=6.28sqrt(1.5/32)}}}

t= 1.36 s



2(d) How many times will the pendulum in 2(c) swing back and forth in one minute?