A sewing machine needle moves with a rapid oscillatory motion, essentially in simpleharmonic motion, as it sews a seam. Suppose the needle moves 9.5 mm from its highest to itslowest position as it makes 36 stiches in 8.0 s. (a) What is the angular frequency, o, of theneedle? (b) What is the maximum speed of the needle? (c) What is the magnitude of themaximum acceleration of the needle? (d) Include a diagram of the situation that indicateswhere the location of the maximum speed and acceleration are located in the motion of theneedle. [

Answered: Image /qna-images/answer/8faa0fb3-e974-40b1-b5bb-2adec9ac02a5.jpg

Answered: A sewing machine needle moves with a…

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)...

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The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi’ vi’ and ai ; the angular frequency of oscillation is ω. (a) Show that the position and velocity of the object for all time can be written as
The equation of motion of a particle in simple harmonic motion is given by: x(t) = 0.1cos(wt), where xis in meters and t is in seconds. At x = 0, the particle's velocity is v -1.256 m/s. The period of oscilation, T, equals 15 sec 0.5 sec 0025 sec: C1 sec 3 sec
One end of a string is fixed. An object attached to the other end moves on a horizontal plane with uniform circular motion of radius R and frequency F. The tension in the string is Fs. If both radius and frequency are doubled, the tension is...?
A physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? The moment of inertia of the pendulum about its axis of rotation is I= 2/5 mR^2
A small bird’s wings can undergo a maximum displacement amplitude of 4.60 cm (distance from the tip of the wing to the horizontal). If the maximum acceleration of the wings is 18.7 m/s2, and we assume the wings are undergoing simple harmonic motion when beating, what is the oscillation frequency of the wingtips?
A piston in a gasoline engine oscillates with simple harmonic motion. The displacement of the piston varies according to x(t) = (6.00 cm) cos (2t + ), where x is in cm and t is in seconds. At t= 0, find: i) the position of the particle, ii) its velocity, iii) its acceleration, iv) the period, and v) the amplitude.
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A particle moves along X-axis according in the equation x = a sin wt + b cos ot, where a, b and o are constants. Show that the motion is S.H.M. Further, if a = 3 cm, b = 4 and o %3D 5 rad/s, find (1) amplitude, (2) period and (3) initial phase.
The function x = (6 m) cos[(4π rad/s)t + π/8 rad] gives the simple harmonic motion of a body. At t =3 s, what are the (a) acceleration, and (b) phase of the motion?
A piston in a gasoline engine is in simple harmonic motion. The engine is running at the rate of 3 600 rev/min. Taking the extremes of its position relative to its center point as ±5.00 cm, find the magnitudes of the (a) maximum velocity and (b) maximum acceleration of the piston.
The position with time of an object is given byx(t)=Acos(ωt)If the amplitude is 1.37 m, and the frequency is 2.9 Hz, what is the object's acceleration at 15.13 seconds?

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