Question

An expression for the period of a simple pendulum with string length ℓ derived using calculus is T = 2(pi)sqrt{ ℓ /g } . Where g is the acceleration due to gravity. Use the data in the table to decide whether or not the pendulum in the experiment can be considered a simple pendulum. Explain your decision.

Suppose have the ability to vary the mass m of the bob and the length f of the string. You decide to to conduct an experiment and motion. Of course, just as any good experimentalist would, you are careful to vary one of these quantities at a time and measure the period of the pendulum, recording the data in the table below realize you can also easily adjust the Amplitude A of the back and forth Mass (kg)Length (m)Amplitude (m) 0.05 0.05 0.05 0.05 0.05 0.05 0.07 0.10 Period (s) 2.00 2.00 2.00 2.80 3.45 4.00 2.00 2.00 4

Answer 1

As you Know the time period of the pendulum is independent of the mass of the pendulum.

You see in the table for l= 1 m T= 2 s

If we change length of the string then chenge in the time period

T'= sqrt(L) ×T here T=2 s for L=1m

L= 2m

T'= sqrt(2) ×2 = 2.82 s

For L=3 m

T'= sqrt(3) ×2=3.46 s

For L=4 m

T'=sqrt(4)×2 = 4 s

We have checked here the values of table follow the shm formula

T=2×π×sqrt(L/g)

For L=1m ,g=9.81 m/s^2

We find T=2 s.

So the pendulum in the experiment can be considered a simple pendulum.