What is the period and frequency of a 10-pound weight oscillating (as a pendulum) on a 5-meter-long rope?
use the formula T = 2*pi*sqrt(L/g)
make sure you use SI units.
I got frequency: 2pi/√ 2
Period: √2/2pi
T is period so you have frequency and period backwards
To find the period and frequency of a pendulum oscillating on a rope, we can use the formula for the period of a simple pendulum:
Period (T) = 2π * √(L / g)
Where:
- T is the period of the pendulum
- L is the length of the pendulum's rope
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
In this case, we have a 10-pound weight oscillating on a 5-meter-long rope. Before we can calculate the period and frequency, we need to convert the weight to mass, as the formula requires it.
Using the conversion factor 1 pound ≈ 0.4536 kilograms, we can convert the weight of 10 pounds to:
Mass (m) = 10 pounds * 0.4536 kg/pound
Now that we have the mass, we can calculate the period using the formula above by substituting the values:
Period (T) = 2π * √(L / g)
= 2π * √(5 m / 9.8 m/s²)
To get the numerical value of the period, we can use a calculator. Finally, the frequency (f) can be calculated by taking the reciprocal of the period:
Frequency (f) = 1 / T
With these calculations, you will have both the period and frequency values for the specified pendulum.