Question

The formula T=2pi sqrt(L/32) gives the time it takes in seconds, T, for a pendulum to make one full swing back and forth, where L is the length of the pendulum, in feet. To the nearest foot, what is the length of a pendulum that makes one full swing in 1.9 s?

Answer 1

Answer:

3 feet.

Step-by-step explanation:

If the length of the pendulum is given by L feet and T gives the time taken by the pendulum to complete a full swing i seconds, then they are related to each other by the relation, $T=2\pi \sqrt{\frac{L}{32} }$ ..... (1)

The relation (1) can be modified to, $\sqrt{\frac{L}{32} }=\frac{T}{2\pi }$

⇒ $L= 32(\frac{T}{2\pi } )^{2}$ ....... (2)

So, if another pendulum takes 1.9 secs to complete a full swing, then it's length will be, L=$32(\frac{1.9}{2*\frac{22}{7} } )^{2}$

=2.92 feet {From equation (2)}

≈ 3 feet. (Answer)

Answer 2

The length of a pendulum is about 3 feet.

Step-by-step explanation:

The given formula is

$T=2\pi \sqrt{(\frac{L}{32})}$

where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

We need to find the  length of a pendulum that makes one full swing in 1.9 s.

Substitute T=1.9 in the given formula.

$1.9=2\pi \sqrt{(\frac{L}{32})}$

Divide both sides by 2π.

$\frac{1.9}{2\pi}=\sqrt{(\frac{L}{32})}$

$0.3024=\sqrt{(\frac{L}{32})}$

Taking square on both sides.

$(0.3024)^2=\frac{L}{32}$

$0.09144576=\frac{L}{32}$

Multiply both sides by 32.

$2.9262=L$

$L\approx 3$

Therefore, the length of a pendulum is about 3 feet.

#Learn more

The period of oscillation of a simple pendulum is T=2pi√4g. measured value of l is 20.0 cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch of 1s resolution. What is the determination of g.

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