The period of a pendulum is the time the pendulum takes to swing back and forth one full time. The function I = 0.81t2 relates the length l in feet of a pendulum to the time t in seconds that it takes to swing back and forth. The convention center in Portland, Oregon, has the longest pendulum in the U.S. The pendulum's length is 90 ft. Find the period for this pendulum.
Question
The period of a pendulum is the time the pendulum takes to swing back and forth one full time. The function I = 0.81t2 relates the length l in feet of a pendulum to the time t in seconds that it takes to swing back and forth. The convention center in Portland, Oregon, has the longest pendulum in the U.S. The pendulum's length is 90 ft. Find the period for this pendulum.
Solution
Given the function I = 0.81t^2, where I is the length of the pendulum in feet and t is the time in seconds it takes to swing back and forth, we can find the period of the pendulum by rearranging the equation to solve for t.
First, substitute I with 90 (the length of the pendulum in feet):
90 = 0.81t^2
Next, divide both sides of the equation by 0.81 to isolate t^2:
t^2 = 90 / 0.81
Calculate the right side:
t^2 = 111.111
Finally, take the square root of both sides to solve for t (the period of the pendulum):
t = sqrt(111.111)
t ≈ 10.54 seconds
So, the period for this pendulum is approximately 10.54 seconds.
Similar Questions
What is the period of a simple pendulum that is 1.13-m long in each situation? In the physics lab
a) The period of a simple pendulum is T = 2𝜋L/g where L is the length of the pendulum and g is the acceleration due to gravity at the pendulum's location. Thus, if a pendulum has a period of T = 1.9 s on Earth where gEarth = 9.8 m/s2, its length isLEarth = gEarthT24𝜋2 = m/s2 s 2 4𝜋2 = m = cm
A grandfather clock uses a physical pendulum to keep time. The pendulum consists of a uniform thin rod of mass M = 1.61 kg and length L = 0.153 m that is pivoted freely about one end, with a solid disk of mass 3M and a radius of L4𝐿4 attached to the free end of the rod. Determine the length L that gives a period of T = 2.45 s
A pendulum is swinging with a period of 0.280 s.What is the frequency of the pendulum?
A simple pendulum has a period of 2 seconds on Earth (g=9.8m/s²). What would be its period on the Moon where g is approximately 1.6m/s²?Select one:a.12.25 sb.0.65 sc.2.44 sd.7.75 s
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.