A two-mass system consists of a piston of mass (m_{1}), connected by two elastic springs, that moves

Question:

A two-mass system consists of a piston of mass $m_{1}$, connected by two elastic springs, that moves inside a tube as shown in Fig. 5.23. A pendulum of length $l$ and end mass $m_{2}$ is connected to the piston as shown in Fig. 5.23.

(a) Derive the equations of motion of the system in terms of $x_{1}(t)$ and $\theta(t)$.

(b) Derive the equations of motion of the system in terms of the $x_{1}(t)$ and $x_{2}(t)$.

(c) Find the natural frequencies of vibration of the system.

image text in transcribed

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Mechanical Vibrations

ISBN: 9780134361925

6th Edition

Authors: Singiresu S Rao

See More Books

Question Posted: May 02, 2024 01:01 AM

See More Questions

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
Developments in Technology Light is incident from air on the end face of a multimode optical fibre at angle of incidence as shown below. n n 1 2 The refractive indices of the core and cladding are...
Include another public method in the Employee class from Pencil and Paper Exercise 3. The method should calculate an Employee objects new salary, which is based on the raise percentage provided by...
A firm has $100 million available for capital expenditures. It is considering investing in one of two projects; each has a cost of $100 million. Project A has an IRR of 20 percent and an NPV of $9...
On any given date, is the money spent equal to, less than, or greater than the budgeted amount? lop5
E 8-7 Subsidiary sells share to outside entities On January 1, 2014, Yasmeen BSC acquired 90,000 out of 100,000 outstanding common shares of Talal BSC for $720,000. The total stockholders equity...
Four factors are thought to possibly influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be...
Plaza, Inc., acqures 80 percent of the outstanding common stock of Stanford Corporation on January 1, 2018, in exchange for $892,000 cash. At the acquisition date, Stanford's total fair value,...
Find the natural frequencies of the system shown in Fig. 5.24, with $m_{1}=m, m_{2}=2 m$, $k_{1}=k$, and $k_{2}=2 k$. Determine the response of the system when \(k=1000 \mathrm{~N} /...
Two masses $m_{1}$ and $m_{2}$, each connected by two springs of stiffness $k$, are connected by a rigid massless horizontal rod of length $l$ as shown in Fig. 5.22. (a) Derive the equations...
What kind of production environment would you expect to see if a company uses a chase strategy? What if it uses a level strategy? LO.1
The residents of the town of Stewart are well-known coffee drinkers. Dunkin Donuts and Starbucks stores supply the residents with over 100,000 cups of hot coffee per week. Recently, coffee drinkers...
Read through the following case study and analyse it by addressing the question that follows. Case study: Adriana Adriana runs a very busy multi-sports coaching company that provides after-school...
Assuming that you were invited to one of your best friends' wedding. Therefore, you decided to purchase a special product or service as a gift for this important event. Based on this scenario, you...
The Department of Commerce, through the Economic Development Administration (EDA), is seeking information to inform the planning and design of the Regional Technology and Innovation Hub (Tech Hubs)...
In frontline management, it is essential to manage time effectively. In the table below, list 3 time-management principles that are relevant to a frontline manager's own work and provide 3 examples...
For an in control process with subgroup data n = 3, X-bar = 100, and R-bar = 3.386, compute the Cp, CPL, CPU, and Cpk if a. LSL = 98 and USL = 102. b. LSL = 93 and USL = 107.5.
Identify one local business that uses a perpetual inventory system and another that uses a periodic system. Interview an individual in each organization who is familiar with the inventory system and...
Minden Company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each $2...
Prepare the adjusting journal entries and Post the adjusting journal entries to the T-accounts and adjust the trial balance. Dresser paid the interest due on the Bonds Payable on January 1. Dresser...
Venneman Company produces a product that requires 7 standard pounds per unit. The standard price is $11.50 per pound. If 3,900 units required 28,400 pounds, which were purchased at $10.92 per pound,...

A two-mass system consists of a piston of mass (m_{1}), connected by two elastic springs, that moves

Question:

7 x1 k 000000 m 8(1) k 000000000000 m2 FIGURE 5.23 Piston-pendulum motions.

Step by Step Answer:

To tackle this problem we need to derive the equations of motion using a combination of Newtons laws of motion and the principle of virtual work a Equ...View the full answer

Mechanical Vibrations

Students also viewed these Engineering questions