Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 16, Problem 53PQ
To determine
Show that Equation 16.50 is a solution to Equation 16.49.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Please Asap
A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h.
a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u.
b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.
If you substitute the expressions for ω1 and ω2 into Equation 9.1 and use the trigonometric identities cos(a+b) = cos(a)cos(b) - sin(a)sin(b) and cos(a-b) = cos(a)cos(b) + sin(a)sin(b), you can derive Equation 9.4.
How does equation 9.4 differ from the equation of a simple harmonic oscillator? (see attached image)
Group of answer choices
A. The amplitude, Amod, is twice the amplitude of the simple harmonic oscillator, A.
B. The amplitude is time dependent
C. The oscillatory behavior is a function of the amplitude, A instead of the period, T.
D. It does not differ from a simple harmonic oscillator.
Chapter 16 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 16.1 - Prob. 16.1CECh. 16.2 - Prob. 16.2CECh. 16.2 - For each expression, identify the angular...Ch. 16.5 - Prob. 16.4CECh. 16.6 - Prob. 16.5CECh. 16.6 - Prob. 16.6CECh. 16 - Case Study For each velocity listed, state the...Ch. 16 - Case Study For each acceleration listed, state the...Ch. 16 - Prob. 3PQCh. 16 - Prob. 4PQ
Ch. 16 - Prob. 5PQCh. 16 - Prob. 6PQCh. 16 - The equation of motion of a simple harmonic...Ch. 16 - The expression x = 8.50 cos (2.40 t + /2)...Ch. 16 - A simple harmonic oscillator has amplitude A and...Ch. 16 - Prob. 10PQCh. 16 - A 1.50-kg mass is attached to a spring with spring...Ch. 16 - Prob. 12PQCh. 16 - Prob. 13PQCh. 16 - When the Earth passes a planet such as Mars, the...Ch. 16 - A point on the edge of a childs pinwheel is in...Ch. 16 - Prob. 16PQCh. 16 - Prob. 17PQCh. 16 - A jack-in-the-box undergoes simple harmonic motion...Ch. 16 - C, N A uniform plank of length L and mass M is...Ch. 16 - Prob. 20PQCh. 16 - A block of mass m = 5.94 kg is attached to a...Ch. 16 - A block of mass m rests on a frictionless,...Ch. 16 - It is important for astronauts in space to monitor...Ch. 16 - Prob. 24PQCh. 16 - A spring of mass ms and spring constant k is...Ch. 16 - In an undergraduate physics lab, a simple pendulum...Ch. 16 - A simple pendulum of length L hangs from the...Ch. 16 - We do not need the analogy in Equation 16.30 to...Ch. 16 - Prob. 29PQCh. 16 - Prob. 30PQCh. 16 - Prob. 31PQCh. 16 - Prob. 32PQCh. 16 - Prob. 33PQCh. 16 - Show that angular frequency of a physical pendulum...Ch. 16 - A uniform annular ring of mass m and inner and...Ch. 16 - A child works on a project in art class and uses...Ch. 16 - Prob. 37PQCh. 16 - Prob. 38PQCh. 16 - In the short story The Pit and the Pendulum by...Ch. 16 - Prob. 40PQCh. 16 - A restaurant manager has decorated his retro diner...Ch. 16 - Prob. 42PQCh. 16 - A wooden block (m = 0.600 kg) is connected to a...Ch. 16 - Prob. 44PQCh. 16 - Prob. 45PQCh. 16 - Prob. 46PQCh. 16 - Prob. 47PQCh. 16 - Prob. 48PQCh. 16 - A car of mass 2.00 103 kg is lowered by 1.50 cm...Ch. 16 - Prob. 50PQCh. 16 - Prob. 51PQCh. 16 - Prob. 52PQCh. 16 - Prob. 53PQCh. 16 - Prob. 54PQCh. 16 - Prob. 55PQCh. 16 - Prob. 56PQCh. 16 - Prob. 57PQCh. 16 - An ideal simple harmonic oscillator comprises a...Ch. 16 - Table P16.59 gives the position of a block...Ch. 16 - Use the position data for the block given in Table...Ch. 16 - Consider the position data for the block given in...Ch. 16 - Prob. 62PQCh. 16 - Prob. 63PQCh. 16 - Use the data in Table P16.59 for a block of mass m...Ch. 16 - Consider the data for a block of mass m = 0.250 kg...Ch. 16 - A mass on a spring undergoing simple harmonic...Ch. 16 - A particle initially located at the origin...Ch. 16 - Consider the system shown in Figure P16.68 as...Ch. 16 - Prob. 69PQCh. 16 - Prob. 70PQCh. 16 - Prob. 71PQCh. 16 - Prob. 72PQCh. 16 - Determine the period of oscillation of a simple...Ch. 16 - The total energy of a simple harmonic oscillator...Ch. 16 - A spherical bob of mass m and radius R is...Ch. 16 - Prob. 76PQCh. 16 - A lightweight spring with spring constant k = 225...Ch. 16 - Determine the angular frequency of oscillation of...Ch. 16 - Prob. 79PQCh. 16 - A Two springs, with spring constants k1 and k2,...Ch. 16 - Prob. 81PQCh. 16 - Prob. 82PQ
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- 11-28. Show from Figure 11-9c that the components of o along the fixed (x) axes are w{ = ℗ cos & + & sin Øsin ¢ w = 8 sin sin cos w = cos 0 + $arrow_forwardQuestion 2 a) A laminar boundary layer profile may be assumed to be approximately of the form u/Ue= f (n)=f(y/8) i) Use an integral analysis with the following two-segment velocity profile, ƒ (n)=(n/6)(10–3n−1³), for 0≤7≤0.293 and ƒ (7) = sin (л7/2) for 0.293≤n≤1, to find expressions for the displacement thickness &*, the momentum thickness e, the shape factor H, the skin-friction coefficient c, and the drag coefficient CD. ii) Derive an expression for the velocity normal to the stream wise direction given that, u/U₂ = f(n). iii) Hence obtain the velocity normal to the stream wise direction for the above two- segment velocity profile.arrow_forwardA double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for describing a double pendulum free to move in a plane in gravity g? Assume the connecting rods are rigid. 4₁ m₁ L₂ m₂²₂ Hint: Let's just assume L₁ 2 2 L = ¼m²³² (0₂² +401² +30₁02 cos(0₁ - 0₂)) + ½ mgl (3 cos 0₁ + cos 0₂). L₂ = 1 and that m₁ = m₂ = m and show that the Lagrangian reduces to :arrow_forward
- P13.28 Normalize the set of functions $„(0) = eino, 0 ≤ 0 ≤ 2π. To do so, you need to multiply the functions by a normalization constant N so that the integral •2π, N N* ² m(0)n(0) do = 1 for m = n.arrow_forwardNote: Make sure your calculator is in radian mode for this problem, and that you switch it back after this problem. There are two particles (1 and 2) that are moving around in space. The force that particle 2 exerts on 1 is given by: F→21(t)=Fxe−(t/T)ı^+Fysin(2πt/T)ȷ^ Where the parameters have the values: Fx=14.2 N, Fy=89 N, T=55 s.We will consider a time interval that begins at ti=0 s and ends at tf=96 s. Find the x component of the impulse from 2 on 1 between ti and tf.arrow_forwardYou measure the oscillation period of a flexible rod to be T= 9.20 ± 0.5 ms. The so-called angular frequency ω is obtained from T by the formula: ω=2pi/T Naturally, your calculator gives you the value ω=683.0 s-1. What is the uncertainty on ω s-1? Include two significant figures.arrow_forward
- Show that the function x(t) = A cos ω1t oscillates with a frequency ν = ω1/2π. What is the frequency of oscillation of the square of this function, y(t) = [A cos ω1t]2? Show that y(t) can also be written as y(t) = B cos ω2t + C and find the constants B, C, and ω2 in terms of A and ω1arrow_forwardThermodynamics and wave. I just want the mcq anwser without justification.arrow_forwardQuestions 1 and 2 please!arrow_forward
- A uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity.Randomized Variables M = 2.4 kgL = 1.6 mx = 0.38 m a) In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point. b) Calculate the rod’s period T in seconds for small oscillations about its pivot point. c) In terms of L, find an expression for the distance xm for which the period is a minimum.arrow_forward11.112 A model rocket is launched from point A with an initial velocity vo of 75 m/s. If the rocket's descent parachute does not deploy and the rocket lands a distance d = 100 m from A, determine (a) the angle a that vo forms with the vertical, (b) the maximum height above point A reached by the rocket, (c) the duration of the flight. Fig. P11.112 400 ftarrow_forwardFind Fnet->C info in added picturearrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
SIMPLE HARMONIC MOTION (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=XjkUcJkGd3Y;License: Standard YouTube License, CC-BY