The length of simple pendulum that makes 12 oscillation/minute is
12oscillations per minute can also be written as:
12/60 oscillation per second
So we get 1oscillation per second
Now ,we know the formula
T=2π√l/g
Put the values in in rhe formula
T=5sec
g=10m/sec
So,
5=2π√l/g
Now squaring both side we get
25=2×2×π×π×l/10
Put value of π as 22/7
Then value of l =6.3m
period=60sec/12=5sec
period=2PIsqrt(length/g) solve for length.
Oh, the simple pendulum is just swinging to the beat of its own drum, huh? Well, to figure out the length of a simple pendulum that makes 12 oscillations per minute, we can use a little math and some laughs.
Let's start by converting 12 oscillations per minute to oscillations per second because who doesn't love some SI units mixed with their humor? Ha! So, 12 oscillations per minute is equal to 12/60 oscillations per second, which simplifies to 0.2 oscillations per second.
Now, let's use a fun little formula to find the length of the pendulum. Brace yourself, here it comes - the period of a pendulum is given by the equation T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Since we're going for 0.2 oscillations per second, that means the period (T) is 1/0.2, which simplifies to 5 seconds. And we know that the acceleration due to gravity is approximately 9.8 m/s² - gravity isn't just a joke, it's real!
Now, let's solve for L in our equation. We have 5 = 2π√(L/9.8). To get L by itself, we'll have some humorous math magic going on. Dividing both sides by 2π and subsequently squaring both sides, we'll find L = (5/2π)² * 9.8.
Now, let's calculate it for some giggles! I mean, accurate scientific calculations. The length of the simple pendulum that makes 12 oscillations per minute is approximately equal to L = 0.061 meters. Ta-da!
So, if you want your pendulum to truly swing to the rhythm of 12 oscillations per minute, make sure its length is around 0.061 meters. And remember, laughter is the best oscillation!
To find the length of a simple pendulum that makes 12 oscillations per minute, you can use the formula:
T = (2π√(L/g))^-1
where T is the time period (in seconds), L is the length of the pendulum (in meters), and g is the acceleration due to gravity (approximately 9.8 m/s²).
To convert minutes to seconds, we need to multiply by 60:
T = 12 oscillations/minute * (1 minute/60 seconds) = 12/60 Hz = 0.2 Hz
Now, solve for L:
0.2 = (2π√(L/9.8))^-1
Rearranging the equation:
(2π√(L/9.8))^-1 = 0.2
Taking the reciprocal of both sides:
2π√(L/9.8) = 5
Squaring both sides:
4π²(L/9.8) = 25
Simplifying:
L/9.8 = 25/(4π²)
Solving for L:
L = (25/(4π²)) * 9.8
Using a calculator, the length of the simple pendulum that makes 12 oscillations per minute is approximately 1.014 meters.
To find the length of a simple pendulum that makes 12 oscillations per minute, we can use the equation:
T = (2π) * √(L / g)
Where:
T is the period of the pendulum (in seconds)
π is pi, approximately 3.14159
L is the length of the pendulum (in meters)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, we want to find the length of the pendulum, so we can rearrange the equation to solve for L:
L = (T / (2π))^2 * g
First, we need to convert the number of oscillations per minute to the period of the pendulum in seconds. There are 60 seconds in a minute, so:
T = (1 minute / 12 oscillations) * (60 seconds / 1 minute)
T = 5 seconds
Now, we can substitute the values into our equation:
L = (5 seconds / (2π))^2 * 9.8 m/s^2
L = (2.5 / π)^2 * 9.8 m/s^2
L ≈ 0.40810 * 9.8 m/s^2
L ≈ 4.00148 m
Therefore, the length of the simple pendulum that makes 12 oscillations per minute is approximately 4.00148 meters.