Physics Laboratory Manual
4th Edition
ISBN: 9781133950639
Author: David Loyd
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 12A, Problem 2PLA
The mass m shown in Figure 12A-1 oscillates on a spring of spring constant k with amplitude A about the equilibrium position yo between the points y = yo + A and y = yo ‒ A. Choose the correct statements about the kinetic energy K, the spring potential energy US, and the gravitational potential energy UG for this motion (Questions 1-4).
2. The gravitational potential energy UG is (a) maximum at y = yo ‒ A. (b) zero at y = yo + A. (c) minimum at y = yo + A. (d) zero at y = yo.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The phase space trajectory of an undamped oscillator is shown below. In the diagram, eachdivision along the position axis corresponds to 0.1 m; along the velocity axis, 0.10 m/s.
What is the angular frequency ?Aof the undamped oscillator? Explain how you can tell.
The equation of motion for a damped harmonic oscillator is s(t) = Ae^(−kt) sin(ωt + δ),where A, k, ω, δ are constants. (This represents, for example, the position of springrelative to its rest position if it is restricted from freely oscillating as it normally would).(a) Find the velocity of the oscillator at any time t.(b) At what time(s) is the oscillator stopped?
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 12A Solutions
Physics Laboratory Manual
Ch. 12A - Prob. 1PLACh. 12A - The mass m shown in Figure 12A-1 oscillates on a...Ch. 12A - The mass m shown in Figure 12A-1 oscillates on a...Ch. 12A - The mass m shown in Figure 12A-1 oscillates on a...Ch. 12A - A spring has a spring constant of k = 7.50 N/m. If...Ch. 12A - A spring of spring constant k = 8.25 N/m is...Ch. 12A - A mass of 0.400 kg is raised by a vertical...
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
- A block of mass m = 2 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is initially at the equilibrium point at x = 0 m where the spring is at its natural length. Then theblock is set into a simple harmonic oscillation with an initial velocity 2.5 m/s at x = 0 cm towards right. Thehorizontal surface is frictionless. a) What is the period of block’s oscillation? b) Find the amplitude A of the oscillation, which is the farthest length spring is stretched to. c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motion graphx(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motion graph.Assume the clock starts from when the block is just released. d) Please find out the block’s acceleration when it is at position x = 5cm. e) On the motion graph you draw for part c), please mark with diamonds ♦ where the kinetic energy of theblock is totally transferred to the spring…arrow_forwardNeed help with part A and B and C pls. Part C asks: If the angular displacement can be written as θ=Ae^(−γt)cosω′t, find how long it takes for the amplitude to be reduced to 1/2 of its original value.arrow_forwardTwo springs of force constants k1 and k2 are attached to a block of mass m and to fixed supports as shown in Fig. 2. The table surface is frictionless. (a) If the block is displaced from its equilibrium position and is then released, show that its motion will be simple harmonic with angular frequency w = √(k1 + k2)/m. (b) Suppose the system is now submersed in a liquid with damping coefficient b , what is the condition that the block will return to itsequilibrium position without oscillation?Sketch a graph to show the behavior of the system in this case.arrow_forward
- 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.arrow_forwardA wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes a distance r from the axle, . (a) Assuming that the wheel is a hoop of mass m and radius R, what is the angular frequency v of small oscillations of this system in terms of m, R, r, and the spring constant k? What is v if (b) r = R and (c) r = 0?arrow_forwardShow,by integration that the moment of inertia of a uniform thin rod AB of mass 3m and length 4a about an axis through one end and perpendicular to the plane of the rod, is 16ma2 The rod is free to rotate in a vertical plane about a smooth horizontal axis through its end A Find i)The raduis of gyration of the rod about an axis through A ii)The period of small oscillations of the rod about its position of stable equilibrumarrow_forward
- Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius8units, with linear speed 3units per second.arrow_forwardThe system in the figure below is in equilibrium, and its free body diagram drawn on the right. The distance, d is 1.14 m and each of the identical spring's relaxed length is l0 = 0.57 m. The mass, m of 0.86 kg brings the point P down to a height h = 15 cm. The mass of the springs are negligible. Calculate the following quantities: (a) The angle ? (b) The force exerted on P by the right spring (c) The force exerted on P by the left spring (d) The total spring length (e) The stretch length (f) The stiffness constant of the springsarrow_forwardA ball attached to a spring is raised 2 feet and released with an initial vertical velocity of 3 feet per second. The distance of the ball from its rest position after t seconds is given by d = 2 cos t + 3 sin t. Show that 2 cos t + 3 sin t = √13 cos(t - θ),where θ lies in quadrant I and tanθ =( 3/2). Use the identity to find the amplitude and the period of the ball’s motion.arrow_forward
- .If one oscillator was out of phase with another oscillator by 45 degrees, what fraction of a 360-degree cycle would it be out of phase: ⅛, ¼, ½ or ¾?arrow_forwardA particle of mass m moving in one dimension has potential energy U(x) = U0[2(x/a)2 (x/a)4], where U0 and a are positive constants. (a) Find the force F(x), which acts on the particle. (b) Sketch U(x). Find the positions of stable and unstable equilibrium. (c) What is the angular frequency of oscillations about the point of stable equilibrium? (d) What is the minimum speed the particle must have at the origin to escape to infinity? (e) At t = 0 the particle is at the origin and its velocity is positive and equal in magnitude to the escape speed of part (d). Find x(t) and sketch the result.arrow_forwardIn an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, θ''max, to the maximum angular velocity, θ'max, is π s^(-1). What is the time needed for the pendulum to complete two oscillations?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
SIMPLE HARMONIC MOTION (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=XjkUcJkGd3Y;License: Standard YouTube License, CC-BY