User Account

All Pages

Find the natural frequencies

Assignment Help Mechanical Engineering
Reference no: EM131787236

Question - Given the equation of motion of a 2-DOF system:

J1θ¨1(t) + 2ktθ1(t) - ktθ2(t) = 0

J2θ¨2(t) + 2ktθ1(t) + 2ktθ2(t) = 0

(1) Rewrite them into matrix form:

(2) From above matrix form, define the coefficient matrix of 777_matrix.jpg as J, define the coefficient matrix of 626_matrix1.jpg as K, define θ = 626_matrix1.jpg, We will have a simplified matrix of form: _____.

In order to have non-zero solution, we need det (-ω2J + K) = 0, express that in its detailed matrix form.

(3) Given J1 = J2 = 1 kg.m2, kt =1 N.m/rad,  find the natural frequencies ω1 and ω2.

(4) Given J1 = J2 = 1 kg.m2, kt = 1N.m/rad, find the amplitude ratio r1 and r2.

Reference no: EM131787236

Questions Cloud

What is the semiannual fixed-rate payment : Assume that the swap in question a requires payments semiannually rather than quarterly. What is the semiannual fixed-rate payment?
Spreadsheet model to calculate net present value of profit : Develop a spreadsheet model to calculate the net present value of profit over a 3-year period, assuming a 4% discount rate.
What strengths do you have as the given kind of leader : What strengths do you have as this kind of leader? What are the weaknesses? Give examples from your experience to illustrate.
Estimate the difference between the centers : Compare the two histograms for the two time periods, and explain what they show. Also estimate the difference between the centers.
Find the natural frequencies : find the natural frequencies - find the amplitude ratio - equation of motion of a 2-DOF system
What must accountants do to ensure that such financial : What must accountants do to ensure that such financial statements serve its' purpose
Number of auto parts must be sold in order to break even : Due to new infrastructure projects and changes in city planning, What number of auto parts must be sold in order to break even?
Discuss the first month of operations of her business : Jane Kent is a licensed CPA. During the first month of operations of her business, the following events and transactions occurred
Compare the two histograms : The histograms show the distribution of the percentages of graduates who, 9 months after graduating, have obtained jobs that require a law degree.

Reviews

Write a Review

Mechanical Engineering Questions & Answers

  Air standard otto cycle with constant specific heats

A six cylinder engine runs at 4000 RPM with a compression ratio of 8:1 and a total clearance volume (total for all 6 cylinders) of 600 mL at TDC. The engine intakes atmospheric air at 100 kPA & 20C. The maximum temperature during the cycle is 1500 C

  Determine the mass flow rate of the liquid stream entering

A fan located within the tower draws in atmospheric air at 17°C, 0.098 Pa, 60% relative humidity with a volumetric flow rate of 110 m3/min. Saturated air exits the tower at 30°C, 0.098 MPa. The power input to the fan is 8 kW. Ignoring kinetic an..

  Determine the maximum tensile stress #t in the angle section

Determine the maximum tensile stress #t in the angle section.

  Calculate the undamped natural frequency

Calculate the undamped natural frequency, the damping ratio, and the damped natural frequency -  Is the system overdamped, underdamped, or critically damped?

  The air temperature in the tank at the final state is 77

a 2m3 rigid tank initially contains air at 100kpa and 22 degree c. the tank is connected to a supply line through valve

  Assume the cost of electricity is 89 cents per kwh

an electrically driven pump operating at steady state is used to draw water from a pond. at the pump inlet the pressure

  What is its initial pressure

An airplane pilot is about to leave a long cross-country trip that will require him to use oxygen. He's noticed that the amount of oxygen in the bottle in the plane is low, so he must refill it from the large supply tank of oxygen in his hanger. The ..

  What would be the cause of this migration reversal

Knowing that the principal radii of curvature of a liquid film were r1 and r2 just before its migration reversal, estimate the driving force of the liquid film migration.

  Heat transfer to the cylinder causes an isothermal

a piston-cylinder with a volume of 0.5 m3 holds 1 kg of nitrogen at a temperature of 261 k. heat transfer to the

  Find the higher and lower heating values of ethane

Find the useful heat generated by the composition of 1kg of ethane in a furnace in 20% excess air if the reactants are at 25oc and the products at 1500k. Assume that only 90% of the carbon goes to completion. And find the higher and lower heating v..

  Determine the vertical deflection b at the free end

The "staircase" frame shown in the figure has a fixed support at the upper end and is free at the lower end. Every member of the frame has length Land flexural rigidity EI. A verticalload P acts at the free end. Determine the vertical deflection b..

  Estimate the apparent viscosity of this fluid

Estimate the apparent viscosity of this fluid when the shear strain rate is 70 s-1, and compare this value with the viscosity of water at the same temperature.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +1-415-670-9521

Phone: +1-415-670-9521

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd