Derive the equation of motion for the string? from a microscopic model. Assume a simple model of
Question:
Derive the equation of motion for the string?
from a microscopic model. Assume a simple model of a string as a set of masses ?m spaced evenly on the x axis at regular intervals of ?x, connected by springs of spring constant k = ?/?x. Compute the leading term in the force on each mass and take the limit ?x ? 0 to get the string wave equation, where ? = ?m/?x. In the same limit show that the energy density of the string is given by eq.?
a2 a,2 y(x, 1) = t (x, t) a2
Step by Step Answer:
Label the vertical displacement of each mass as y y j Some relations between derivatives ...View the full answer
Related Video
In Physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. In this video, the concept of force and torque is demonstrated with the practical application of changing the flat tire of the car.
Students also viewed these Physics questions
-
Derive the equation of motion for the system shown in Figure. Assume small angles of oscillation, and neglect the rod mass. What relation among L1, L2, m, and k must be satisfied for the system to be...
-
Derive the equation of motion for the lever system shown in Figure P4.54, with the force f as the input and the angle θ as the output. The position θ = 0 corresponds to the...
-
The mass m in Figure is attached to a rigid rod having inertia I about the pivot and negligible pivot friction. The input is the displacement z. When z = θ = 0, the spring is at its free...
-
help me with questions 10, 11 and 12 to answer them for practiceolin data structures Given the following linked list definitions: struct listRec! string name; listRec *link, ;: nodeType *begin; Code...
-
"Rocket Man" has a propulsion unit strapped to his back. He starts from rest on the ground, fi res the unit, and accelerates straight upward. At a height of 16 m, his speed is 5.0 m/s. His mass,...
-
On the first day of the fiscal year, a company issues a $2,500,000, 4%, five-year bond that pays semiannual interest of $50,000 ($2,500,000 4% ), receiving cash of $2,400,000. Journalize the bond...
-
During your audit of the financial statements of The Gary Manufacturing Company for the year ended December 31, 1999, you find that at January 1, 1999, the company had installed the following...
-
1. Describe the pros and cons of the UP approach versus XP and Scrum development approaches to upgrading the existing systems or developing new ones. Do the pros and cons change if the systems are...
-
When a field goal kicker kicks a football as hard as he can at 45 to the horizontal, the ball just clears the 3-m-high crossbar of the goalposts 45.7 m away. (a) What is the maximum speed the kicker...
-
Assume that on January 1, 20X1, Trans Global Airlines leases two used Boeing 737s from Aircraft Lessors Inc. The eight-year lease calls for payments of $10,000,000 at each year end. On January 1,...
-
A violin A-string of length L = 0.33 m with total mass 0.23 g has a fundamental frequency (for the lowest mode) of 440 Hz. Compute the tension on the string. If the string vibrates at the fundamental...
-
Show that the energy density on a string u(x, t), defined in eq.? obeys the conservation law?u/?t +?S/?x = 0, where S (x, t) = ??y?y? is the energy flux, the energy per unit time passing a point x....
-
Let S be the solid obtained by rotating the region shown in the figure about the -axis. Sketch a typical cylindrical shell and find its circumference and height. Use shells to find the volume of S....
-
1. Bartholemew Incorporated uses a job-order costing system and its total manufacturing overhead applied always equals its total manufacturing overhead. In February the company completed job G43C...
-
Prior to beginning work on this discussion, read the 2017 Sarbanes Oxley Compliance Survey Links to an external site. from Protiviti consulting firm, and the Section 302: Corporate Responsibility for...
-
A company signs a lease acquiring the right to use property for five years. Lease payments of $17156.31 are to be made annually at the end of this year and the next four years. The discount, or...
-
Sandra has ccalculated that her iinvestment of $3,000 will grow to $100,000. If she has a rate of 9% (which is compunded monthly), how longoing in years will.it tare for shandra to have her $100,000?
-
Reflection on A Real-Life Executive Compensation Scheme: Please skim through the articles below, you can refer to other academic/reliable articles:...
-
Assume that a small town uses a referendum to overcome the free-ridership problem and determine how its residents might value a new water filtration system for its public water supply. The voting...
-
At the beginning of its fiscal year, Lakeside Inc. leased office space to LTT Corporation under a seven-year operating lease agreement. The contract calls for quarterly rent payments of $25,000 each....
-
A cart that is rolling at constant velocity on a level table fires a ball straight up. a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or...
-
Anita is running to the right at 5 m/s in FIGURE Q4.8. Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anita, both balls are approaching her at 10 m/s. Which ball...
-
Zack is driving past his house in FIGURE Q4.10. He wants to toss his physics book out the window and have it land in his driveway. If he lets go of the book exactly as he passes the end of the...
-
A positive charge q = +8 nC is at the origin, and a second positive charge q = +12 nC is on the x axis at a = 4 m, Find the net electric field (a) at point P, on the x axis at x=7 m, and (b) at point...
-
8. Hooten Carpentry had the following accounts and account balances after adjusting entries. Assume all accounts have normal balances. Prepare the adjusted trial balance for Hooten Carpentry as of...
-
Explain at least one major difference that exists today between US GAAP and IFRS on the accounting for foreign currency transactions. Be specific.
Study smarter with the SolutionInn App