One ring to rule them all. N identical beads (mass m) can move along the ring...

One ring to rule them all. N identical beads (mass m) can move along the ring of radius R. Each bead is connected
to the one behind it and to the one in front of it by a spring of constant k. Find all normal
frequencies.

Solutions

Expert Solution

genius_generous answered 2 months ago

Next > < Previous

Related Solutions

Consider a particle of mass m that can move in a one-dimensional box of size L...

Consider a particle of mass m that can move in a one-dimensional box of size L with the edges of the box at x=0 and x = L. The potential is zero inside the box and infinite outside. You may need the following integrals: ∫ 0 1 d y sin ⁡ ( n π y ) 2 = 1 / 2 , for all integer n ∫ 0 1 d y sin ⁡ ( n π y ) 2 y = 1...

Evaluate the following integral using the Midpoint Rule M(n), the Trapezoidal Rule T(n), and Simpson's Rule...

Evaluate the following integral using the Midpoint Rule M(n), the Trapezoidal Rule T(n), and Simpson's Rule S(n) using nequals4. Integral from 2 to 6 StartFraction dx Over x cubed plus x plus 1 EndFraction Using the Midpoint Rule, M(4)equals

A mass of 1.1kg is attached to a spring and constrained to move without friction along...

A mass of 1.1kg is attached to a spring and constrained to move without friction along the x-axis. The mass is attached to a spring of spring constant 80?? N m ; one end of the spring is attached to a fixed point along the x-axis while the other is attached to the mass. The equilibrium position of the mass is the origin. The mass has a position as a function of time which can be expressed: ?(?)=?cos(??+?) x (...

The particle has a mass of 0.6 kg and is confined to move along the smooth...

The particle has a mass of 0.6 kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Assume the particle contacts only one side of the slot at any instant. The arm has an angular acceleration of θ¨ = 3 rad/s2 when θ˙ = 2 rad/s at θ = 30∘. (Figure 1) Part A Determine the magnitude of the force of the rod on the particle when θ = 30∘. Express...

Two billiard balls with the same mass m move in the direction of one another. Ball...

Two billiard balls with the same mass m move in the direction of one another. Ball one travels in the positive x-direction with a speed of V1i, and ball two travels in the negative x-direction with a speed of V2i. The two balls collide elastically, and both balls change direction after collision. If the initial speeds of the balls were v1i=2.0m/s and v2i =1.0m/s, what would be the final speed and direction of ball two, v2f, in m/s? Thank...

One particle whose mass is defined by m is moving along a certain line in the...

One particle whose mass is defined by m is moving along a certain line in the region x>0 is subjected to a conservative net force given by the following equation: F(x)= F₀x eˣ^²/²ᴸ^² The constants F and L are both positive real quantities with appropriate physical dimensions. Find the formula for the corresponding U(x), with the given assumption that the limₓ↠∞U(x)=0. Secondly, we know that the particle is launched from an initial location x₀>>>L towards x=0. (the >>> mean that...

A 1.005 m chain consists of small spherical beads, each with a mass of 1.00 g...

A 1.005 m chain consists of small spherical beads, each with a mass of 1.00 g and a diameter of 5.00 mm, threaded on an elastic strand with negligible mass such that adjacent beads are separated by a center-to-center distance of 10.0 mm. There are beads at each end of the chain. The strand has a spring constant of 28.8 N/m. The chain is stretched horizontally on a frictionless tabletop to a length of 1.50 m, and the beads at...

Let's suppose we are pulling a box of mass m along a horizontal floor. All sides...

Let's suppose we are pulling a box of mass m along a horizontal floor. All sides of the box have the same type of surface (same coefficient of friction between any side and the floor). In one case, the contact surface is much larger (first picture) and in another, it is much smaller. Will there be any difference in the force of friction? Why?

A car of mass M and a small truck of mass 3M are travelling along two...

A car of mass M and a small truck of mass 3M are travelling along two roads perpendicular to each other as shown.The car and the truck collide at the intersection at O. The speed of the truck just before collision is VT =15.0m/s. Immediately after the collision, the wreckage moves as a single mass with Vf =12.0m/s as shown. Using conservation of momentum: [a] Find the value (in degrees) of θ? A car of mass M and a small...

The uniform line charge density extends over entire ring λ=1.96E-6 C/m Mass of ring M=0.13 kg....

The uniform line charge density extends over entire ring λ=1.96E-6 C/m Mass of ring M=0.13 kg. Radius of ring R=0.67 m. Radius of Magnetic field region, a=0.41 m. Magnetic field, B=1.61 T. The magnitude of the angular velocity of the wheel after the field is suddenly switched off is w= radians/sec.? The moment of inertia of a loop is MR2.

Subjects