How do you find the gravity at a place using a pendulum using only a graph given its time period and length?

Question

We have to investigate the dependance of time period of a pendulum on its length and hence determine the acceleration due to gravity (using a graph). Thanks for helping!

Answer 1

Start with the formula for the period of a pendulum:

T = (2π)sqrt(L/g)

Use algebra to solve for "g":

g = (2π/T)²(L)

Now make a table with 3 columns: "T", "L", and "g".  In each row, put in the "T" and the "L" taken from some point on the graph.  In the "g" column, put in the calculated value of "g" (based on the above formula).

In theory, you should get the same value for "g" in every row.  (In a real experiment, you'll probably values that differ slightly.)

Answer 2

The oscillating period T, the time from one point in the swing and back again to that same point, depends in part on the g value.  The equation is...

T = 2pi sqrt(L/g); so T^2 = 4pi^2 L/g = (1/g)KL  and 2TdT = (1/g)K dL  K = 4pi^2 to simplify the equation a bit.

Then dL/dT = 2gT/K, which is the slope of the L vs T graph at any point T on the graph.  

Now collect the data for the graph.  Conduct multiple swings of the same pendulum, but at different lengths L = l1, l2, l3, etc.  Time the periods T = t1, t2, t3, etc. for each length.  Plot these p(l,t) for each length and period.

Pick a period T = t and measure the slope dL/dT at that point  Then g = ((dL/dT)K)/(2T) = (dL/dT)4pi^2/2T = (dL/dT)(2pi^2)/T  And there you have it.  You measured dL/dT from the graph at point T = t; so you can solve for g.

When you swing the pendulum, time the first oscillation at each length and do several swings at each length.  Then take the average period for each length.  That will minimuze measuring errors.

Answer 3

Time-period=2*pi*(l/g)^1/2    from graph u can see value of T corresponding to diff values of L...By above formula u can find value of g.....for diff values of T and l all values of g will be approx same