Question

In: Statistics and Probability

The period T of a simple pendulum is given by T=2π√L/g where L is the length...

The period T of a simple pendulum is given by T=2π√L/g where L is the length of the pendulum and g is the acceleration due to gravity. Assume that g = 9.80 m/s^2 exactly, and that L, in meters, is lognormal with parameters μL = 0.6 and σ^2L=0.05. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

Find the mean of T.

Find the median of T.

Find the standard deviation of T.

Solutions

Expert Solution


Related Solutions

Q1: Consider the simple pendulum system, the length of the pendulum is ‘l’ and mass ‘m’...
Q1: Consider the simple pendulum system, the length of the pendulum is ‘l’ and mass ‘m’ has simple harmonic motion. Find the equation of motion using 2 approaches: Newtonian and Lagrangian. What do you conclude?
Consider a simple plane pendulum of mass m and length l (the mass swings in a...
Consider a simple plane pendulum of mass m and length l (the mass swings in a vertical plane). After the pendulum is set into motion, the length of the string is decreased at a constant rate, ??/?? = −? = ?????. The suspension point remains fixed. (a) Compute the Lagrangian and Hamiltonian for the system. [4] (b) Compare the Hamiltonian and the total energy- is the energy conserved? Why/Why not? [2]
on another planet a simple pendulum has a length of 90.0 cm oscillates with a period...
on another planet a simple pendulum has a length of 90.0 cm oscillates with a period of 1.7 seconds. 1. compute the planet’s accerleration due to gravity and comment on the planet’s gravity as compared to Earth’s gravity. 2. on this same planet. what would be the period of oscillation if the pendulum had a length of exactly 2.00 meters?
A simple pendulum with mass m = 1.6 kg and length L = 2.79 m hangs...
A simple pendulum with mass m = 1.6 kg and length L = 2.79 m hangs from the ceiling. It is pulled back to an small angle of θ = 10.7° from the vertical and released at t = 0. A)What is the period of oscillation? B)What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? C)What is the maximum speed of the pendulum? D)What is the angular displacement at t = 3.62...
Part One: A simple pendulum of length l =0.800 has a mass =0.250kg. What is the...
Part One: A simple pendulum of length l =0.800 has a mass =0.250kg. What is the tension in the string when it is at angle theta =12.5°? Show your force diagram and work to support your answer. Part Two: What is the period T of the motion of the pendulum in Part One? Assume the period is independent of angle theta.
A simple pendulum with mass m = 2.3 kg and length L = 2.67 m hangs...
A simple pendulum with mass m = 2.3 kg and length L = 2.67 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.4° from the vertical and released at t = 0. What is the maximum speed of the pendulum? 4) What is the angular displacement at t = 3.57 s? (give the answer as a negative angle if the angle is to the left of the vertical) 5) What is the...
A simple pendulum with mass m = 1.3 kg and length L = 2.62 m hangs...
A simple pendulum with mass m = 1.3 kg and length L = 2.62 m hangs from the ceiling. It is pulled back to an small angle of ? = 11.6° from the vertical and released at t = 0. What is the period of oscillation? What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? What is the maximum speed of the pendulum? What is the angular displacement at t = 3.67...
A simple pendulum with mass m = 1.5 kg and length L = 2.49 m hangs...
A simple pendulum with mass m = 1.5 kg and length L = 2.49 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.5° from the vertical and released at t = 0. What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? What is the maximum speed of the pendulum? What is the angular displacement at t = 3.67 s? (give the answer as a...
Suppose a particular simple pendulum of length l_0 has a period of T_0 for small oscillations...
Suppose a particular simple pendulum of length l_0 has a period of T_0 for small oscillations here on Earth. (a) Suppose the original pendulum is set up with the same length l_0 on the surface of a new planet, Uzaz, and it oscillates with a period 5/4 as long as the period of Earth. Given the gravitational acceleration here on Earth is 9.8 m/s^2, what is the gravitational acceleration (g)(v) at the surface on Uzaz? (b) If the radius of...
A simple pendulum of length 0.50 m has a 0.30-kg bob. At t = 0, the...
A simple pendulum of length 0.50 m has a 0.30-kg bob. At t = 0, the bob passes through the lowest position in its motion, and at this instant it has a horizontal speed of 0.39 m/s . A. What is the maximum angular displacement ϑmax away from vertical that the pendulum reaches? B. What is the magnitude of the bob's linear speed v when it has angular displacement ϑmax/2?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT