The period of a pendulum is the time it takes to swing from left to right and back again.
The period T seconds, of a pendulum is directly proportional to the square root of its length, Lcm.
When L=25, T=1
Find a formula for T in terms of L.
T = 2pi*sqrt(L/g).
T = 1 sec. = Period.
L = Length in cm.
g = 980 cm/s^2.
To find a formula for T in terms of L, we need to determine the constant of proportionality that relates T and the square root of L.
We are given that when L = 25 (in cm), T = 1 second. This provides us with one set of values for L and T.
Since T is directly proportional to the square root of L, we can write the following proportion equation:
T ∝ √L
To remove the proportionality symbol, we introduce a constant k:
T = k√L
Using the given values, we can substitute L = 25 and T = 1 into the equation:
1 = k√25
Simplifying further:
1 = 5k
Now we can solve for k:
k = 1/5 = 0.2
Substituting this value of k back into the equation:
T = 0.2√L
Therefore, the formula for T in terms of L is T = 0.2√L.