3. Three simple harmonic motions are given by y, = 2 sin(ust – 30°),y2 = 5 sin(at + 30°), and y3 = 4 sin(wt + 90°). If they are addedtogether, find (a) the resultant amplitude, (b) the initial phase angleof the resultant, and (c) the resultant equation of motion.4. Two waves having amplitudes of 5 and 8 units and equalfrequencies come together at a point in space. If they meet with aphase difference of 57/8 rad, find the resultant intensity relative tothe sum of the two separate intensities.

As per our guidelines we can solve only a single problem. For the second problem you can post the…

Answered: Three simple harmonic motions are given…

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

The position of x of an oscillating particle as a function of time t is given by x= A cos (Bt) where A and B are constants. What are the physical dimension of those constants?
A weight of 32 lb stretches a spring 6ft. The weight is pulled down 2ft below the equilibrium position and then released. What initial velocity v0 given to the weight would have the effect of doubling the amplitude of the vibration? Use g=32 ft/sec 2. (Type an exact answer, using radicals as needed.)
The motion of a simple harmonic oscillator is described by the following equation and conditions: x(t) = A cos(wt + ø) A = 21 cm, w > 0 x(0) = 15cm v(0) = 2.0 cm/s What is the phase constant o ? 46° 71° -44° 21° O -112°
Maps O New Tab 5. A pendulum consists of a solid sphere of radius R = 10.0 cm and mass M = 90.0 kg attached to a rod of mass m = 30.0 kg and length L. The pendulum swings freely about an axis o perpendicular to the rod and the solid sphere's center, as shown in the figure. If the pendulum is to have a period of 2.47 s for small oscillations. (a) what is the length of the rod L? (b) If the system is pulled aside to angle 0 = 67° and released, what is the maximum value for the angular velocity?
Problem 2: Special sections of roadway are sometimes paved with “rumble strips” to alert inattentive drivers. In a particular case the grooves are spaced L = 0.26 m apart and the depth of each groove is d = 0.35 cm. As you drive over this rumble strip, the tires of your car oscillate about their equilibrium positions with a frequency of f = 68.6Hz. Refer to the figure, which is not drawn to scale. Part (b) Find the vertical position of the tire, in centimeters, at the time t = 1.85 s. Part (c) With your tire oscillating at a frequency of f = 68.6 Hz and the distance between grooves L = 0.26 m, what is the speed of your car, in kilometers per hour?
SA-1 The small angle approximation says that if 0 << 1 rad, then sin(0) ≈ 0, where is in radians. Recall that the % error in using this approximation is given by: % error approximate - exact exact x 100 (a) What is the % error in using the small angle approximation for the sine function, for an angle of 1 degree? (b) What is the % error in using the small angle approximation for the sine function, for an angle of 30 degrees? (c) What is the % error in using the small angle approximation for the sine function, for an angle of 80 degrees?
A mass of 0.38 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.26 m)cos[(16 rad/s)t]. Determine the following. %3D (a) amplitude of oscillation for the oscillating mass How does the amplitude of oscillation compare to the magnitude of the maximum displacement from equilibrium? m (b) force constant for the spring N/m (c) position of the mass after it has been oscillating for one half a period m (d) position of the mass one-third of a period after it has been released (e) time it takes the mass to get to the position x = -0.10 m after it has been released
s An atom in a molecule oscillates about its equilibrium position with a frequencyof 2.00 * 1014Hz and a maximum displacement of 3.50 nm.(a) Write an expression giving x as a function of time for this atom,assuming that x = A at t = 0. (b) If, instead, we assume that x = 0at t = 0, would your expression for position versus time use a sinefunction or a cosine function? Explain.
Determine the amplitude, period, and phase shift of y = 4 sin (2x - 2π/3). Then graph one period of the function.
Two particles oscillate in simple harmonic motion with amplitude A about the centre of a common straight line of length 2A. Each particle has a period of 1.5 s, and their phase constants differ by 4 rad. (a) How far apart are the particles (in terms of A) 0.5 s after the lagging particle leaves one end of the path? Enter the exact answer in terms of A. ab sin (a) Ω
The motion of a body is described by the equation 4.90 sin (0.170πt) where t is in s and y is in m. (a) Find the amplitude.(b) Find the period.(c) Find the frequency.(d) Find the displacement at t = 5.00 s.(e) Find the displacement at t = 30.0 s.
Suppose the water depth during low tide at a certain bay is about 4.0 m, and at high tide it is about 10.0 m. The natural period of oscillation is about 12 hours, and on particular day, high tide occurred at 5:45 a.m. Find the amplitude (in meters) of the model. Find the period (in hours) of the model. hr If the model is a cosine function, it is translated 5.75 units -Select--- v and 7 units --Select--- v Find a function involving the cosine function that models the water depth D(t) (in meters) as a function of timet (in hours after midnight) on that day. D(t) =

Recommended textbooks for you

College Physics

Physics

ISBN:

9781305952300

Author:

Raymond A. Serway, Chris Vuille

Publisher:

Cengage Learning

University Physics (14th Edition)

Physics

ISBN:

9780133969290

Author:

Hugh D. Young, Roger A. Freedman

Publisher:

PEARSON

Introduction To Quantum Mechanics

Physics

ISBN:

9781107189638

Author:

Griffiths, David J., Schroeter, Darrell F.

Publisher:

Cambridge University Press

College Physics

Physics

ISBN:

9781305952300

Author:

Raymond A. Serway, Chris Vuille

Publisher:

Cengage Learning

University Physics (14th Edition)

Physics

ISBN:

9780133969290

Author:

Hugh D. Young, Roger A. Freedman

Publisher:

PEARSON

Introduction To Quantum Mechanics

Physics

ISBN:

9781107189638

Author:

Griffiths, David J., Schroeter, Darrell F.

Publisher:

Cambridge University Press

Physics for Scientists and Engineers

Physics

ISBN:

9781337553278

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Lecture- Tutorials for Introductory Astronomy

Physics

ISBN:

9780321820464

Author:

Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden

Publisher:

Addison-Wesley

College Physics: A Strategic Approach (4th Editio…

Physics

ISBN:

9780134609034

Author:

Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Three simple harmonic motions are given by y, = 2 sin(ast – 30°), y2 = 5 sin(at + 30°), and y3 = 4 sin(st + 90°). If they are added together, find (a) the resultant amplitude, (b) the initial phase angle of the resultant, and (c) the resultant equation of motion.