a simple pendulum with the length of 2.08m oscillates. the acceleration of gravity is 9.8 m/s^2.how many complete oscillations does the pendulum make in 3.75 min?
Get the period P from:
P = sqrt(L/g)
Then compute (225 seconds)/P
That will be the number of oscillations.
27. A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g= 9.80 m/s2. Find (a) the period of the pendulum and (b) its length
To find the number of complete oscillations the pendulum makes in 3.75 minutes, we need to calculate the time period of oscillation and then divide the total time by the time period.
The time period (T) of a simple pendulum can be calculated using the formula:
T = 2π√(L/g)
Where:
T = Time period
π = Pi (approximately 3.14159)
L = Length of the pendulum
g = Acceleration due to gravity
Given:
Length of the pendulum (L) = 2.08 m
Acceleration due to gravity (g) = 9.8 m/s^2
Total time = 3.75 minutes
First, we need to convert the total time from minutes to seconds:
Total time in seconds = 3.75 minutes × 60 seconds/minute
Next, we can calculate the time period using the given length and acceleration due to gravity:
T = 2π√(L/g)
T = 2π√(2.08/9.8)
Now, we can substitute the values in to find the time period:
T ≈ 2π√(0.2122)
T ≈ 2π(0.4608)
T ≈ 2.893 seconds
Finally, we can find the number of complete oscillations by dividing the total time in seconds by the time period:
Number of oscillations = Total time in seconds / Time period
Number of oscillations = (3.75 minutes × 60 seconds/minute) / 2.893 seconds
Calculating this expression, we find:
Number of oscillations ≈ 77.493 oscillations
Therefore, the simple pendulum makes approximately 77.493 complete oscillations in 3.75 minutes.
To find the number of complete oscillations that a pendulum makes, we need to use the formula for the period of a pendulum. The period (T) is the time it takes for the pendulum to complete one full oscillation. The formula for the period of a simple pendulum is:
T = 2π√(L/g)
Where:
T = period of the pendulum
L = length of the pendulum
g = acceleration due to gravity
Given:
Length of the pendulum, L = 2.08m
Acceleration due to gravity, g = 9.8 m/s^2
Let's calculate the period (T) first:
T = 2π√(L/g)
T = 2 * π * √(2.08 / 9.8) [Substituting the given values]
T ≈ 2 * 3.1416 * √(0.212) [Evaluating the square root]
T ≈ 2 * 3.1416 * 0.4601 [Evaluating the square root]
T ≈ 2.8824 seconds [Evaluating the multiplication]
Now, we need to convert the time given from minutes to seconds.
3.75 minutes = 3.75 * 60 seconds
3.75 minutes ≈ 225 seconds
To find the number of complete oscillations in the given time, we divide the total time (in seconds) by the period of the pendulum (in seconds):
Number of oscillations = Total time / Period
Number of oscillations = 225 seconds / 2.8824 seconds
Number of oscillations ≈ 78.10
Therefore, the pendulum makes approximately 78 complete oscillations in 3.75 minutes.