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.

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.

Name: If you substitute the expressions for ω1 and ω2 into Equation 9.1 and
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: 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 th

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter16: Fundamentals Of Light

Section: Chapter Questions

Problem 77A

See similar textbooks

Related questions

Q: How does temperature affect the time measured by a pendulum clock? More precisely, consider a clock…

A: solution is given as

Q: Marianne puts her favorite Bon Jovi disc in her CD player. If it spins with a frequency of 1800…

A: Given that, ω=1800 rvolutions per minut=1800 rpmω=1800×2π60 rad/s=188.49556 rad/s

Q: An oscillating body takes 1.2 seconds to complete four cycles. What is the (a)period, (b)frequency,…

Q: The one-dimensional harmonic oscillator has the Lagrangian L = mx˙2 − kx2/2. Suppose you did not…

A: Given data: The Lagrangian of one-dimensional harmonic oscillator, L=12mx.2-12kx2 The motion…

Q: A massless spring of constant 40N/m is attached vertically to a table. A 5-g balloon is filled with…

Q: A 10-kg steel ball is tied to a string attached to a ceiling. If the length of the string is 45 cm,…

A: Given, A 10-kg steel ball is tied to a string attached to a ceiling. Length of string , l = 45 cm =…

Q: A spring (k = 61.5 N/m) hangs vertically with its top end fixed. A mass attached to the bottom of…

A: Spring constant,

Q: Part A,b

A: Part bThe angular frequency of the vibration of the atom is,Substitute the values,

Q: Consider a ball of 100g dropped with zero velocity from the height of 2m. Estimate its total energy…

A: As per guidelines we are suppose to do only first three subpart form multipart question. Kindly post…

Q: The chemical bond between the two atoms in a diatomic oxygen molecule acts very much like a spring,…

Q: (a) Musicians in an orchestra tune their instruments to what is called “concert A,” a frequency of…

A: The frequency of an oscillation is the number of oscillations per second. Its Si unit is Hz. It is…

Q: If one oscillator was out of phase with another oscillator by 45 degrees, what fraction of a…

A: If one oscillator is out of phase with another oscillator by 45° So Oscillator 1 reaches its maximum…

Q: 4.5 In aerodynamics and fluid mechanics, the functions u(x,y) and v(x,y) in f(z) = u(x,y) + i v(x,…

Q: Ch. 13 - Problem 69 in Wolfson) A particle of massmhas potential energy givenbyU=ax2, where a is a…

Q: y=0.05sin(3×3.14x-18×3.14t+C) If at t=0 an element at x=0 has a vertical displacement y=-0.025 m and…

A: y=0.05sin(3×3.14x-18×3.14t+C)if at t=0 an element at x=0vertical displacement y=-0.025 m

Q: Here on Earth you hang a mass from a vertical spring and start it oscillating with amplitude 1.8 cm.…

A: Given: The amplitude of the system on the earth is 1.8 cm. The period of the system on the earth is…

Q: (Section B) A gun barrel of mass 500kg has a recoil spring of stiffness 3,00,000 N/m. If the barrel…

Q: A cell of mass (M) moves to the top and is attached to a Corona virus of mass (m) by a neglected…

A: Given:- r = constant θ = generalized coordinates. degree of…

Q: I am very confused because I was taught that for a series, you would calculate it by adding…

A: Here, to remove your calculation let us derive the equivalent capacitance of the series and parallel…

Q: The oxygen molecule (O2) may be regarded as two masses connected by a spring. In vibrational motion,…

A: Given that mass of the oxygen atom and vibration energy of oxygen atom and also given the value of…

Q: Write the equations that describe the simple harmonic motion of a particle moving uniformly around a…

A: Simple Harmonic Motion is defined as the projection of uniform circular motion upon the diameter of…

Q: 1) Take the derivative of this function to find the force function associated with it. 2)…

Q: After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0…

A: Write the given values with the suitable variables. l=46 cm=0.46 mn=98t=145 s Here, l is the length,…

Q: The period of oscillation of molecules is of the order of 10-15s. The corresponding linear and…

Q: Which of the following is not equal to the unit of energy? a.) J b.) Nm c.) kg*m^2/s^2 d.) W/s…

A: Energy is the ability of doing work . It's unit is Joules

Q: A simple pendulum is constructed using a string 85 cm long and a ball having a mass of 50 grams. At…

A: Masses of ball m1 and m2 = 50 gm and 100 gm Number of vibrations in 38 sec = 20 Length of strings l1…

Q: With simple harmonic motion, the reciprocal of the period is called the frequency. The frequency,…

A: Given : V = 210 sin(100πt)

Q: spring stiffn

Q: C2 C3 Question 6/10 ميز هذا السؤال Determine the energy stored in C, when C1 15 µF, C2 10 µF, C3 =…

A: In the given circuit, We have to determine the energy stored in capacitor C1.

Q: A tube of length 1.2 m, closed at one end and open at the other, vibrated in its second mode of…

Q: 1. A)Write down the second law as Hooke’s Law, and derive the solution for a frictionless…

A: A)newton's second law of motionF = mass * acceleration ma = F using hooke's lawF = k * xTherefore,…

Q: for what mass will the horizontal, frictionless, mass-spring harmonic oscillator system have a…

A: Given that, Frequency, f=2Hz Spring constant, k=9.8N/m Let the mass be m.

Q: The chemical bond between the two atoms in a diatomic oxygen molecule acts very much like a spring,…

A: The expression for the reduced mass of the system is,

Q: An electron undergoes simple harmonic motion with the acceleration shown below:…

A: Given that acceleration of a electron ax(t)=−a max sin(2t/T) a max = 5839 m/s2 time period T = 316 S…

Q: 6) Consider a bob attached to a vertical string. At t 0, the bob is displaced to a new position…

Q: Assuming that the vibrations of a 14N2 molecule are equivalent to those of a harmonic oscillator…

A: Since the vibration of molecule are those of harmonic oscillator, the zero point energy is…

Q: A massless spring is hanging vertically. With no load on the spring, it has a length of 0.24 m. When…

Q: A horizontal spring mass system oscillates on a frictionless plane. At time t=0, it is moving left…

A: Given:- Time period t = 2 sec T = 2πω ⇒2πT=2π2 = π rad/sec.

Q: A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left end of the string…

A: Given:- A string has length L= 2.0 m The tension T = 60 N The linear density 0.080 kg/m The ring…

Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

Topic Video

Question

100%

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, A_mod, 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.

V = 1 + 2
= A cos (w1 t) + A cos (wz t) ---- Equation 9.1
%3D
1
Wbeat
2
W1 = Way +
-
w2 = Wav
Wbeat
1
1
V = A cOS
Wav
Wbeat
+ A CoS
Wav
Wbeat
+
= A [{cos (Way t) cos
Wpeat t
sin (way t) sin
Wbeat
2
1
{cos (wav t) cos
Wbeat t
+ sin (way t) sin
Wbeat t}|
V = 2 A cos (wav t) cos
Wbeat
2
-
(금
1
Wbeat
2
Amod (t) = 2 A cos
= Amod (t) cos (Wav t)
Equation 9.4
-----

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

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

Item 9 Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area. on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation B = (10 dB) log (1) where Io = 1.0 × 10-12 W/m². Part A What is the value of log (1,000,000)? Express your answer as an integer. ► View Available Hint(s) The logarithm of x, written log(x), tells you the power to which you would raise…
This is phyiscs question i attached the soloution also. I don't need this soloution that is from chegg and this is wrong. Plz provide me a clear handwritten and perfect soloution in one hour and take a thumb up plz
Sping-Undergraduate-2020-A X M Inbox (3,685)-sadik1261@gm X Mail - MUHAMMAD.ISLAM@c X Course Home MasteringPhysics: HW6 A session.masteringphysics.com/myct/itemView?assignmentProblemlD=136302988&offset%3Dnext Apps (1) ইমাম মাহদী কব... YouTube to MP3 Co... phone cover for mo... |Online Services Fo... AGARWAL-PHY-166 KHW6 Item 6 A 22-g bullet traveling 290 m/s penetrates a 1.5 kg block of wood and emerges going 135 m/s Part A If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges? Express your answer to two significant figures and include the appropriate units. HA Value Units %3D Submit Request Answer Provide Feedback II
What do you multiply the DBH of a tree by to get the distance required for tree to be considered "In" when doing a variable radius plot? 2.25 2.75 3.0 3.75
Could you please explain how to do this? I really dont understand it and could use a clear explanation.
MTNSA-Take Care Mz. l N21% 10:51 PM Let a =i b=l and c=1.The quantity be wrthen witanhca ))? -ez+abex) partigular con in,a 7orm values andz.whot is the volve wz? to 07 w 首 A Note OCR Share More ...
For the triangle shown, the value of sine is Select one: 3m а. 0.8575 O b. 0.5145 5m О с. 1.666 O d. 0.600
x = xo + voxt += axt², Vx = Vox + axt, (v²) = (vox)² + 2axx, y = Yo + Voyt + ½ ayt², vy = voy + Ayt, (v²) = (voy)² + 2a,Ay, 1 m Vox = Vo cose, voy = vo sin , g = 9.8. sec² Problem 1: A deer wishes to jump over a fence that is 2.1 m high. If the deer jumps with an initial speed of 11 m/sec at an angle of 41°. a) What is the maximum height the deer reaches above the ground? Answer: 2.7 m b) What range of distances can the fence be placed over which the deer will be successful at clearing it? Answer: Xmin = 3.3 m and xmax = 8.9 m. кутах d 18 2.1m ^Xmin Xmax ↑
4. The equation y' = A sin(kx-at+)is the same as a. π y = -A sin(kx- ct + 7/7 - ) 2 b. y = A cos(kx - at) y=-Acos(kx - at) d. e. y = -A sin(kx -at - - श 2 y = A sin(kx - out + 1, 3A 2 wall at one end while the o changed by changing along the stri 3π)
For the triangle shown, the value of sine is Select one: 3m O a. 0.600 O b. 0.5145 5m O c. 0.8575 O d. 1.666
(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)
Consider the equation s=s0+v0t+a0t2/2+j0t3/6+s0t4/24+ct5/120 , were s is a length and t is a time. What are the dimensions and SI units of (a) s0 , (b) v0 , (c) a0 , (d) j0 , (e) s0, and (f) c ?