To measure the magnitude of the acceleration due to gravity g in an unorthodox manner, a student places a ball bearing on the concave side of a flexible speaker cone ( Figure 1). The speaker cone acts as a simple harmonic oscillator whose amplitude is A and whose frequency f can be varied. The student can measure both A and f with a strobe light. Take the equation of motion of the oscillator as y(t) = A cos (wt + p), where w 2πf and the y axis points upward. If the ball bearing has mass m, find N (t), the magnitude of the normal force exerted by the speaker cone on the ball bearing as a function of time. Your result should be in terms of A, either f (or w), m, g, a phase angle o, and the constant . ► View Available Hint(s) N (t) = IVE ΑΣΦ ?

To measure the magnitude of the acceleration due to gravity g in an unorthodox manner, a student places a ball bearing on the concave side of a flexible speaker cone ( Figure 1). The speaker cone acts as a simple harmonic oscillator whose amplitude is A and whose frequency f can be varied. The student can measure both A and f with a strobe light. Take the equation of motion of the oscillator as y(t) = A cos (wt + p), where w 2πf and the y axis points upward. If the ball bearing has mass m, find N (t), the magnitude of the normal force exerted by the speaker cone on the ball bearing as a function of time. Your result should be in terms of A, either f (or w), m, g, a phase angle o, and the constant . ► View Available Hint(s) N (t) = IVE ΑΣΦ ?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A small piece of rounded stone perforated for threading is sliding on a wire which is hanging freely in the shape of a cosh function. Assume the stone moves with no friction. For very small displacements in x, what is the frequency of oscillation? You may use for the height of the wire and thus the height of the stone as a function of x the Taylor series expansion of cosh. G(x) =1 + x2/2 + x4/24 + ...
decreases to (1/3) of its original value, then thel executing S.H.M is V. If the amplitude is Q. 58: The maximum velocity of a particle doubled and the time period of oscillation particle 18V (b) 6V (a) 12V (d) 3V
I need help with this please
Consider the solution tothe harmonic oscillator given above by x(t)=Ccos(wt−v) Prove tha tx(t0)=x(t0+2piw) In other words, the solution has the same value at time:t0 and at time:t0+2piw regardless of what value we have for ?0. The value 2piw is then the period T of the harmonic oscillator.
A 1 kg mass is attached to a horizontal spring with stiffness 4 N/m. Initially, the spring is at rest. At time t = 0 an external force, measured in Newtons, F(t) = 3 cos(2t) is applied to the spring. The damping constant is zero. The function y(t) describes the displacement, measured in meters, of the mass from the rest position at time t measured in seconds. Choose all correct statements: a. y" + 4y = 3 cos(2t). O b. y" + 4y = 0. c. The amplitude of the oscillations of y(t) is 3. d. The system is at resonance.
An electron undergoes simple harmonic motion with the acceleration shown below: ax(t)=−amaxsin(2t/T) with amax=5839 ms2 and T=316 seconds. Assuming that the only motion is oscillatory (ignoring overall translation), what is the maximum speed of the electron? What is the amplitude of the electron's position?
An undamped harmonic oscillator of mass m and spring constant k oscillates with an amplitude A. In terms of A, at what postion x is the speed of the oscillator, v, is half of its maximum speed v, max Hint: Set-up the energy equation at any postion. What is the maximum energy of the oscillator?
Use the following transformation to solve the linear harmonic oscillator problem: Q = p + iaq, P = (p − iaq) / (2ia)
A simple device to measure projectile speed consists of a block of ballistic material of mass M attached to a wall by a spring (of negligible mass; we don't know its spring constant) and resting on a flat, frictionless surface. The device is impacted by a projectile of mass m, which embeds itself in the material, after which the two move together in simple harmonic motion with amplitude A and period T. a) During the collision for this system, is energy conserved? Is momentum in the horizontal direction conserved? b) After the collision, is energy conserved? What about momentum? c) What was the initial velocity v of the projectile before the collision (again in terms of m, M, A, and T)? d) Compute v for m = 5 g, M = 1 kg, A = 5 cm, and T = 0.201 s.
A mass of 458 g stretches a spring by 7.2 cm. The damping constant is c = 0.34. External vibrations create a force of F(t)= 0.4 sin 5t Newtons, setting the spring in motion from its equilibrium position with zero velocity. What is the imaginary part v, of the complex root of the homogeneous equation? Use g-9.8. Express your answer in two decimal places.
If there is an oscillator with M = 160 kg, K = 80N/m (a) what is the period of the %3D %3D motion?
A spring with spring constant k= 7 N/m is horizontal and has one end attached to a wall and the other end attached to a M = 4 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is D = 1 N · s/m, and the forcing function is F(t) = 2 sin(4t). a. Find the long-term motion of the attached mass if initially the mass is at rest at the equilibrium position. That is, what remains of the solution after all exponentially decaying terms have effectively reached zero. Long-term motion: æ(t) = b. Find the long-term motion of the attached mass if initially the mass is pulled 0.1 metres away from the equilibrium position and is released. Long-term motion: æ(t) =