Concept explainers
This problem explores the nonlinear pendulum discussed qualitatively in Conceptual Example 13.1. You can tackle this problem if you have experience with your calculator’s differential-equation solving capabilities or if you’ve used a software program like Mathematica or Maple that can solve differential equations numerically. On page 228 we wrote Newton’s law for a pendulum in the form I d2θ/dt2 = −mgL sin θ. (a) Rewrite this equation in a form suitable for a simple pendulum, but without making the approximation
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Essential University Physics Volume 1, Loose Leaf Edition (4th Edition)
Additional Science Textbook Solutions
Conceptual Physics (12th Edition)
The Cosmic Perspective Fundamentals (2nd Edition)
College Physics
Lecture- Tutorials for Introductory Astronomy
The Cosmic Perspective
Conceptual Physical Science (6th Edition)
- Either all parts or none... I vll definitely upvotearrow_forwardI need help for this exercise.arrow_forwardAfter landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0 cm. The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 145s. What is the magnitude of the gravitational acceleration on this planet? gPlanet=(?)m/s^2arrow_forward
- After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm . The explorer finds that the pendulum completes 109 full swing cycles in a time of 142 s . How does one determine the magnitude of the gravitational acceleration on this planet, expressed in meters per second?arrow_forwardQ91: Write the following function as a linear differential equation system of rank 1 and find the solutions: x" + tx" + 2t³x' – 5tª = 0arrow_forwardanswer only a..14arrow_forward
- Your grandfather clock's pendulum has a length of 0.9930 m. a. If the clock runs slow and loses 23 s per day, how should you adjust the length of the pendulum? Note: due to the precise nature of this problem you must treat the constant g as unknown (that is, do not assume it is equal to exactly 9.80 m/s2). Express your answer to two significant figures and include the appropriate units. Enter positive value in case of increasing length of the pendulum and negative value in case of decreasing length of the pendulum.arrow_forwardTwo pendulums have the same dimensions (length L) and total mass 1m2. Pendulum A is a very small ball swinging at the end of a uniform massless bar. In pendulum B, half the mass is in the ball and half is in the uniform bar. Find the period of each pendulum for small oscillations. Which one takes longer for a swing?arrow_forwardAfter landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 50.0 cm. She finds that the pendulum makes 100 complete swings in 136 s. What is the value of g on this planet? (10.7 m/s³)arrow_forward
- 787878 A particle moves that is defined by the parametric equations x = 3t² - 1 y = t³ - 3t² + t - 3 (where x and y are in meters, and t is in seconds). a. Compute the radial component of the acceleration (m/s^2) at t = 2 seconds. b. Compute the transverse component of the acceleration (m/s^2) at t = 2 seconds.arrow_forwardIn the experiment, you will study an oscillator called a "torsion pendulum." In this case, the restoring "force" is the torsion constant of the wire that suspends the weight X and the inertial term is the rotational inertia of the suspended mass. You will compare the periods of a suspended sphere and of a suspended cube. The rotational inertia of a sphere is Is = 1/10msD^2, where ms is the mass of the sphere and D is its diameter. The rotational inertia of a cube is Ic = 1/6mcS^2, where mc is the mass of the cube and S is the length of its side. If the cube and the sphere are suspended from the same wire, what is the expected ratio of their periods, Tc/Ts? Assume that D = S, ms = 0.20kg, and mc = 0.5 kg.arrow_forwardA ferris wheel is 50 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o' clock position on the ferris wheel is level with the loading platform. the weel completes 1 full revolution in 2 minutes. The function h=f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude in meters, and midline, and period? How high are you off the ground after 1 minute?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning