P1a.m₁ = m₂ m₂ = 2mk₁=k₂k₂ = 2k[m₂μ₂ = −k₂ (u₂-u₂)[m₁ü₁ = −k₂(µ₁ − u₂)-₁₁[m₂ï₁ + (k₂ +k₂)µ₁ −k₂u₂ = 0[m₂²₂ −k₂U₁ +k₂U₂ = 0Setting u₁ = U₁ cos at, u₂ = U₂ cos cot[_m₂w²U₁ + (k₂ +k₂)U₁ - k₂U₂ = 0|_m₂w²U₂ −k₂U₁ + k₂U₂ = 0[(3k-mw³)U₁-2kU₂ = 0[-kU₁ + (k-ma²)U₂ = 0(3k-ma²) -2k160²30/-0=-k(k-ma²)(3k-ma²)(k-ma²) - 2k² = 0(mw² ) ² − 4k (mw² )+k² = 0Dividing by m² and solve for ²(~³²)³² - 4 ( # )(~³²) + ( # ) ³ - 0mmkm|«² = (2 ± √3)P1b.[(3k-ma²)U₁-2kU₂ = 0[-kU₁ + (k-mw³)U₂ = 0By setting U₂=1,m=20kg, k=1000 N/m|U₁ =2k(3k-ma²)(note: The 2nd eqn will givethe same answer){0.73205)77(¹)=at a = 3.66[-2.73205)1at a = 13.66[u₂ (t))[[u₁₂ (1))[U₁cos(art-a₂)]- [7²) 7(²2) ] {U₂ cos(art-a₂))77With u₁(0)1,u₂ (0)=-1,₁ (0) = 0,u₂ (0) = 0,determine U₁,U₁,a₁ and ₂ For the 2 DOF system shown with m₁ = m, m₂ = 2m and k₁=k, k₂ = 2k, determine: (a) The naturalfrequencies and the corresponding mode shapes. (b) The response of the system, u₁(t) and u₂(t).For this part, assume m = 20 kg, k = 1000 kg, and initial conditions:101 = 1, 02 = -1; 1=0,02 = 0. (c) Plot u, (t) and u₂(t) of part b on the same graph.иции[mi] Tui (t)K=m₂ Tuz(t)

Answered: Image /qna-images/answer/79c5116a-8aa1-458e-adb2-893b712cd6e0.jpg

For the 2 DOF system shown with m₁ = m, m₂ = 2m and k₁=k, k₂ = 2k, determine: (a) The natural frequencies and the corresponding mode shapes. (b) The response of the system, u₁(t) and u₂(t). For this part, assume m = 20 kg, k = 1000 kg, and initial conditions: 101 = 1, 02 = -1; 1=0,02 = 0. (c) Plot u, (t) and u₂(t) of part b on the same graph. иции [mi] Tui (t) K= m₂ Tuz(t)

For the 2 DOF system shown with m₁ = m, m₂ = 2m and k₁=k, k₂ = 2k, determine: (a) The natural frequencies and the corresponding mode shapes. (b) The response of the system, u₁(t) and u₂(t). For this part, assume m = 20 kg, k = 1000 kg, and initial conditions: 101 = 1, 02 = -1; 1=0,02 = 0. (c) Plot u, (t) and u₂(t) of part b on the same graph. иции [mi] Tui (t) K= m₂ Tuz(t)

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

Related questions

Q: A string of 1 m length clamped at both ends is plucked in the middle to generate a standing wave.…

A: Standing waves are those waves which vibrates instead of propagate. This is achieved usually in a…

Q: = o/ k where k = (k, +k, +k? )"². Here k = (k,,k,k,) is the wavevector of the V phase Show that the…

A: Given, Plane wave

Q: A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released…

Q: Two identical circular cylinders, each with mass m and radius r according to the figure, are…

A: Given: Two similar Cylinder with, Radius = r mass = m Icylinder = mr2/2

Q: cillator, show the raising

A: The proof of commutation relations as,

Q: A string of 1 m length clamped at both ends is plucked in the middle to generate a standing wave.…

A: Given: Length, L=1m Frequency f=10Hz

Q: Design a 4MGH CLAPP sinusoidal oscillator using a MOSFET. Make a drawing of the final circuit with…

A: Given that,CLAPP sinusoidal oscillator fo= 4MHz .......eqn 1Here,…

Q: A string of 1 m length clamped at both ends is plucked in the middle to generate a standing wave.…

A: The standing wave is the resultant of two progressive waves moving in opposite directions. Therefore…

Q: Find the total energy of the string in its nth characteristic mode, assuming the string is in a pure…

A: Let's assume the mass of the string is m, length is L , the tension in the string is given by T .…

Q: om Problem 3(a). Ple à(0) = 0 for the D uld this ride end?

A: Given as, l1=30cm l2=70cm n=480Hz

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: In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is…

A: Given that, frequency f=200 HzL=1.2 mLinear density, μ=1.6 g/m=1.6×10-3 kg/mWhere, n=4Mass,…

Q: In Problem 28 nd the critical points and phase portrait of the given autonomous rst-order…

A: The objective of the question is to find the critical points and phase portrait of the given…

Q: A periodic vibration at x = 0, t = 0 displaces air molecules along the x direction by smax = 1.8E-05…

Q: 11. A mass weighing 64 pounds stretches a spring 0.32 foot. The mass is initially released from a…

A: Given: The weight of the mass is W = 64 lbs The distance that the spring stretches is x = 0.32 ft…

Q: A string of length 0.282 m is producing a standing wave of period 0.017 second with 6 harmonics. The…

Q: What are the phase constants for the harmonic oscillator with the position function x (t) given in…

Q: by using this wavefunction az? 4 = Ce find the lowest energy level of harmonic oscillator

A: Given, wavefunction is, ψ=Ce-αx22 And hamiltonian of the harmonic oscillator is,…

Q: A block of mass m, attached to a spring of force constant k, undergoes a simple harmonic motion on a…

A: If a spring mass system undergoes SHM on horizontal surface: Law of conservation of energy is…

Q: A thin 6-m string of mass 50.0 g is fixed at both ends and under a tension of 89 N. If it is set…

Q: An oscillator with a mass of 1kg is driven by a force with Fo= 20N , has a natural frequency wo 100…

Q: In the given wave function below, what is the position of the particle at x = 0.250 m at t = 0.300…

A: The wave function is given by : y(x,t) =( 0.500 m) Cos2π(x0.500 m - t0.400 s)

Q: A string of 1 m length clamped at both ends is plucked in the middle to generate a standing wave.…

A: Given : Length of the string, L = 1 m Wave generated by plucking in the middle so, Length, L = 0.5 m…

Concept explainers

Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

Question

100%

P1a.
m₁ = m₂ m₂ = 2m
k₁=k₂k₂ = 2k
[m₂μ₂ = −k₂ (u₂-u₂)
[m₁ü₁ = −k₂(µ₁ − u₂)-₁₁
[m₂ï₁ + (k₂ +k₂)µ₁ −k₂u₂ = 0
[m₂²₂ −k₂U₁ +k₂U₂ = 0
Setting u₁ = U₁ cos at, u₂ = U₂ cos cot
[_m₂w²U₁ + (k₂ +k₂)U₁ - k₂U₂ = 0
|_m₂w²U₂ −k₂U₁ + k₂U₂ = 0
[(3k-mw³)U₁-2kU₂ = 0
[-kU₁ + (k-ma²)U₂ = 0
(3k-ma²) -2k
160²30/-0
=
-k
(k-ma²)
(3k-ma²)(k-ma²) - 2k² = 0
(mw² ) ² − 4k (mw² )+k² = 0
Dividing by m² and solve for ²
(~³²)³² - 4 ( # )(~³²) + ( # ) ³ - 0
m
m
k
m
|«² = (2 ± √3)
P1b.
[(3k-ma²)U₁-2kU₂ = 0
[-kU₁ + (k-mw³)U₂ = 0
By setting U₂=1,
m=20kg, k=1000 N/m
|U₁ =
2k
(3k-ma²)
(note: The 2nd eqn will give
the same answer)
{0.73205)
77(¹)
=
at a = 3.66
[-2.73205)
1
at a = 13.66
[u₂ (t))
[[u₁₂ (1))
[U₁cos(art-a₂)]
- [7²) 7(²2) ] {U₂ cos(art-a₂))
77
With u₁(0)1,u₂ (0)=-1,₁ (0) = 0,u₂ (0) = 0,
determine U₁,U₁,a₁ and ₂

For the 2 DOF system shown with m₁ = m, m₂ = 2m and k₁=k, k₂ = 2k, determine: (a) The natural
frequencies and the corresponding mode shapes. (b) The response of the system, u₁(t) and u₂(t).
For this part, assume m = 20 kg, k = 1000 kg, and initial conditions:
101 = 1, 02 = -1; 1=0,02 = 0. (c) Plot u, (t) and u₂(t) of part b on the same graph.
иции
[mi] Tui (t)
K=
m₂ Tuz(t)

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

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

Consider the following figure: a forced oscillator system is shown in the figure where C = 8.0x10^-6 F, L = 2.0×10^-2 H, R = %3D %3D 75 ohm and V(t) = Vo cos wt (volt) a. Write down the equation for forced oscillation. b. Calculate the impedance and resonant frequency. c. Show the maximum potential at which the inductance appears at the frequency w == wo(1 – 1/2Q3)/2 . IR V,= Vo cosot Va
Why is it only possible to produce the odd harmonics in a system with oneopen end and one closed end.
1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 8.0 kg/s. The mass is initially released from rest with displacement 0.30 m from equilibrium. Determine the displacement x(t) as a function of time without assuming weak dissipation. Numerically compute all quantities. (b) The time for transients to become negligible is typically taken to be 5t, where the time constant t is the time required for the amplitude to decay to e-1 of its initial value. Taking the displacement amplitude to be approximately A = 0.30 m, (which holds for weak damping), determine the amplitude at time 5t. = Xoe¬Bt where xo
In the vibrational motion of HI, the iodine atom essentially remains stationary because of its large mass. Assuming that the hydrogen atom undergoes harmonic motion and that the force constant is 317 N m-1, what is the fundamental vibration frequency?