# Differential Equations

Consider the system shown below of two masses of mass m, coupled together between two fixed walls via springs with varying spring constants.

Let x(t) and y(t) be the horizontal displacements of the two masses as a function of time.

(a)Write down a system of differential equations for x'' and y''.

(b)For the case when m = 1, k1 = 1 and k2 = 2, calculate the eigenvalues associated with this system, which are associated with the characteristic frequencies of vibration.

(c)Plot the eigenvalues as a function of k2 over the range 0 < k2 < 3. Discuss the physical interpretation of the changes to the eigenvalues as k2 is increased.

1. 👍 0
2. 👎 0
3. 👁 77
1. k2=0

1. 👍 0
2. 👎 0
posted by uu

## Similar Questions

1. ### Calc. Based Physics

10.1 Three uniform spheres with masses m1 = 6.0 kg, m2 = 2.0 kg , and m3 = 4.0 kg are fixed at the positions shown in the diagram. Assume they are completely isolated and there are no other masses nearby. m_1 | | 3cm | m_2-- P ^ |

asked by Sarah on March 27, 2017
2. ### Physics

The two masses shown in the figure are each initially 1.80 m above the ground, and the massless frictionless pulley is fixed 4.8 m above the ground. (mA = 1.5 kg and mB = 3.4 kg.) What maximum height does the lighter object reach

asked by Megan on September 21, 2014
3. ### physics

A block of mass M1 = 15 kg is lying on a horizontal friction-less surface is connected to a string passing over a friction-less pulley. A mass of M2 = 25 kg is hanging at its other end as shown in the figure below. (i) Find the

asked by trei-sha on April 13, 2015
4. ### Physics(Rotational Energy)

Suppose three masses are arranged as shown, connected by a rodless mass. (2 kg)-------(6 kg)--------(4 kg) 2m 3m a) If this object is free to rotate in space, about what point will it spin? b) A small mass (m=0.1 kg) drops

asked by ChristinaNguyen on July 16, 2012
5. ### Differential Equations

Consider the spring - mass system, shown in Figure 4.2.4. consisting of two unit masses suspended from springs with spring constants 3 and 2, respectively. Assume that there is no damping in the system. Show that the displacements

asked by Daoine on May 13, 2014
6. ### Physics

The Atwood Machine consists of two masses suspended form a fixed pulley. If the first mass is 0.55kg and 0.8kg, (a) what is the acceleration of the system? (b) What is the magnitude of the tension in the string? (consider the

asked by Raphael Grenfell on April 20, 2016
7. ### science

Two balls of masses 5 kg and 15kg are separated by a fixed distance of 0.8m. find the position of the centre of mass of system

asked by raynold on February 21, 2012
8. ### physics

Find the threshold energy that the incident neutron must have to produce the reaction 1 n 0 + 4 He 2---> 2 H 1 + 3 H 1 For this, like the 1 n 0

asked by jaimie on February 16, 2007
9. ### Physics

Two masses, mA = 40.0 kg and mB = 55.0 kg, are connected by a massless cord that passes over a pulley that is free to rotate about a fixed axis. This device is known as an Atwood’s Machine. The pulley is a solid cylinder of

asked by Cheese on October 23, 2014
10. ### Physics

A 2 kg mass on a horizontal friction-free air track is accelerated by a string attached to a 100 kg mass hanging vertically from a pulley as shown. Compare the accelerations when the masses are interchanged, that is, for the case

asked by Andrew on January 9, 2010

More Similar Questions