В.Find the oscillation frequency of the ball.Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t)) follows a certain form.Also, since the energy of the system is conserved, then dE/dt = 0. Consider a solid uniform ball of mass m and radius R rollingwithout slipping near the bottom of a frictionlesshemispherical fishbowl of radius r as shown. The balloscillates about the center of the fishbowl. Set thegravitatio nal potential energy to be zero at the bottom of thebowl.r cosr(1 - cos 0)A.Express the total energy of the ball as a function of the ball's distance from the center x and itsvelocity.Hint 1: Since the ball is rolling without slipping, its angular velocity can be expressed in terms of its linearvelocity, and it has translational and rotational energy.Hint 2: In writing gravitational potential U, use the approximation cos 0 1- then use SOH-CAH-TOAto rewrite 0 in terms of x and r, then use sin 0 - 0 to eliminate the variable 0.

Given,mass of ball =mradius=RA. Translational and rotational kinetic energy of the…

Answered: В. Find the oscillation frequency of…

Similar questions

H In a damped oscillator, let m = 250 g, k=85 N/m, and b=0.070 kg/s. In how many periods of oscillation the mechanical energy of the oscillator drop to one-half of its initial value?
A sphere moves in simple harmonic motion with a frequency of 1.00 Hz and an amplitude of 4.90 cm. What is the maximum magnitude of acceleration (in m/s2) of the sphere? Where in the motion does the maximum acceleration occur?
A cart of mass m = 1.6 kg placed on a frictionless horizontal surface and connected to a spring with spring constant 6 N/m. The damping force strength is given by b = 255 g/s. The cart is pulled away 16.5 cm and released. k m 'b a. Calculate the time required for the amplitude of the resulting oscillations to fall to 1/7 of its initial value. 24.4 b. How many oscillations are made by the cart in this time? 7.51
A 1.3 kg block is attached to a spring with spring constant 13 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 39 cm/s. Part A: What is the amplitude of the subsequent oscillations? Part B: What is the block's speed at the point where x=0.40 A?
A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.80 Hz. Block B rests on it, and the coefficient of static friction between the two is µ. = 0.640. What maximum amplitude of oscillation can the system have if block B is not to slip? cm Ms P
A block of mass 1.80 kg is attached to an ideal spring with spring constant 340 N/m, and it oscillates on a frictionless surface. As it passes through its equilibrium position (spring is neither stretched or compressed), it’s moving at 12.0 m/s. Part A. What is the amplitude of the block's oscillation? Part B. What is the maximum acceleration of the block during its osciation?
Chapter 15, Problem 24 Z Your answer is partially correct. Try again. In the figure, two springs are joined and connected to a block of mass 40.3 kg that is set oscillating over a frictionless floor. The springs each have spring constant k = 242 N/m. What is the frequency (in Hz) of the oscillations? Number Units THz the tolerance is +/-2%
6. The pendulum shown is a nonlinear dynamic system. Get a dynamic system linear around 0 = 0° for this dynamic system and the transfer function corresponding linearized. Consider m = 10kg; L = 0.5m. Also, note that in the axis of rotation there is a torsion spring of stiffness with k = 100N*m / rad. m,L k 2m
At an outdoor market, a bunch of bananas is set into oscillatory motion with an amplitude of 20.0 cm on a spring with a force constant of 16.0 N/m. It is observed that the maximum speed of the bunch of bananas is 43.0 cm/s. What is the weight of the bananas in newtons? N
Problem HW7.2 A block of mass m = 1.8 kg is fastened to an unstrained horizontal spring whose spring constant is k = 85 N/m. The block is given a displacement of +0.15 m, where the sign indicates that the displacement is along the +x-axis, and then released from rest. (a) Find the angular frequency of the resulting oscillatory motion. Does this number change if the initial displacement is larger? Explain with a sentence or two. (b) Use concept of energy to determine the maximum speed of the block. Explicitly state which initial and final positions you used for energy states. (c) Use the concept of force to set up a free body diagram and Newton's Second Law equation to determine the magnitude of the maximum acceleration of the block.
You are sitting on a surfboard that is riding up and down on some swells. The board’s vertical displacement is given by Y = (1.2m)cos((t)(1/2s) +π/6) Find amplitude, angular frequency, phase constant, frequency, and period of the motion. Where is the surfboard at t = 1.0s? Find the velocity and acceleration as functions of time t. Find the initial values of the position, velocity, and acceleration of the surfboard.
Chapter 15, Problem 051 GO In the figure, a stick of length L = 1.9 m oscillates as a physical pendulum. (a) What value of distance x between the stick's center of mass and its pivot point o gives the least period? (b) What is that least period? L/2 (a) Number Units (b) Number Units udy Click if you would like to Show Work for this question: Open Show Work

SEE MORE QUESTIONS

В. Find the oscillation frequency of the ball. Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t)) follows a certain form. Also, since the energy of the system is conserved, then dE/dt = 0.