A simple 2.45 m long pendulum oscillates.
How many complete oscillations does this
pendulum make in 6.05 min?
The acceleration due to gravity is 9.8 m/s2
.
P =2pi* sqrt(L/g) = 6.28 sqrt(2.45/9.8) = 3.14s.
6.05min. * 60s./min. = 363 s.
363s * 1osc./3.14s = 115 Oscillations.
To find the number of complete oscillations, we need to determine the period of the oscillations (i.e., the time taken for one complete oscillation).
The period (T) of a pendulum is given by the formula:
T = 2π√(L/g)
Where:
T = period of the pendulum
L = length of the pendulum
g = acceleration due to gravity
Given:
L = 2.45 m
g = 9.8 m/s^2
Let's calculate the period first:
T = 2π√(2.45/9.8)
T ≈ 2π√(0.25)
T ≈ 2π(0.5)
T ≈ π
The period of the pendulum is approximately equal to π seconds.
Now, to find the number of complete oscillations in 6.05 minutes (or 6.05 * 60 = 363 seconds):
Number of oscillations = (total time) / (period)
Number of oscillations = 363 / π
Number of oscillations ≈ 115.33
Therefore, the pendulum makes approximately 115 complete oscillations in 6.05 minutes.
To find the number of complete oscillations made by the pendulum in 6.05 minutes, we first need to determine the period of the pendulum.
The period of a pendulum is the time it takes for one complete oscillation. It can be calculated using the formula:
T = 2π * √(L / g)
Where:
T is the period of the pendulum (in seconds)
π is the mathematical constant pi (approximately 3.14159)
L is the length of the pendulum (in meters)
g is the acceleration due to gravity (in m/s^2)
In this case, the length of the pendulum (L) is given as 2.45 meters, and the acceleration due to gravity (g) is given as 9.8 m/s^2.
Let's calculate the period of the pendulum:
T = 2π * √(2.45 / 9.8)
T = 2π * √(0.25)
T ≈ 2π * 0.5
T ≈ π
So, the period of the pendulum is approximately π seconds.
Next, we can calculate the number of complete oscillations in 6.05 minutes. To convert minutes to seconds, we multiply the given time by 60.
Number of oscillations = (Total time in seconds) / (Period of pendulum in seconds)
Total time in seconds = 6.05 minutes * 60 seconds/minute
Number of oscillations = (6.05 * 60) / π
Using the value of π approximately as 3.14159, we can calculate:
Number of oscillations ≈ (6.05 * 60) / 3.14159
Number of oscillations ≈ 364.17
Therefore, the pendulum makes approximately 364 complete oscillations in 6.05 minutes.