Problem 1: Recall the two-mass system from a previous problem set, in which you deter- mined the (stable) equilibrium point of the system. (a) Let y be the distance of the bead from the ceiling. From the earlier problem, rewrite U(0) so that the potential energy is a function of this variable y, instead of 0. Also, given the expression for the equilibrium angle, find the equilibrium position yo for this system. (b) Expand U(y) in a Taylor series around Yo to show that for small oscillations, U(y) can be written in the Hooke's Law form ky², and determine the "effective spring constant" k. (c) Write the total kinetic energy T of the system as a function of y. Compare your kinetic and potential energy for this system to the energy expressions in the SHO, and determine this system's angular frequency for small oscillations. M b Ꮎ m

Problem 1: Recall the two-mass system from a previous problem set, in which you deter- mined the (stable) equilibrium point of the system. (a) Let y be the distance of the bead from the ceiling. From the earlier problem, rewrite U(0) so that the potential energy is a function of this variable y, instead of 0. Also, given the expression for the equilibrium angle, find the equilibrium position yo for this system. (b) Expand U(y) in a Taylor series around Yo to show that for small oscillations, U(y) can be written in the Hooke's Law form ky², and determine the "effective spring constant" k. (c) Write the total kinetic energy T of the system as a function of y. Compare your kinetic and potential energy for this system to the energy expressions in the SHO, and determine this system's angular frequency for small oscillations. M b Ꮎ m

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.56P: The stiffness of the ideal spring that is compressed by the slider C is k = 250 N/m. The spring is...

See similar textbooks

Similar questions

Q/ Find the reaction Force of system in A,B,C Shown in fig
4. What are the three equations of equilibrium for a general coplanar-force system?
A 64-lb weight is attached to a vertical spring, causing it to stretch 3 in. upon coming to rest at equilibrium. The samping constant for the system is 3 lb·sec/ft. An external force F(t) = 3 cos(12t) lb is applied to the weight. Find the steady-state for the system. Note that g≈32 ft/s2
The hanging mobile pictured above consists of two masses, m1 and m2, suspended from a uniform 10 cm long rod, which is in turn suspended from the ceiling at an angle of 70 as pictured above. The mass m1 is 0.02 kg, while the mass of the rod is mr = 0.01 kg. Assuming the mobile is in a state of static equilibrium, find the value of mass m2.
According to the shape, the rod of length ℓ and weight W can rotate freely around A, and the other end is connected to a body of weight W by a thread. Find the system equilibrium using the principle of virtual work.
Analytically solve and find the equilibrium. The given above is its experimental value.
If the forces in a system were drawn graphically on scale, which among the force systems is in equilibrium? Note: F is the force in the system, R is the resultant. A) A, C, and D only B) B and E only C) A, D, and E only D) All of them are in equilibrium. E) None of them are in equilibrium.
Suppose three forces with magnitudes of 198 N, 275 N, and 205 N are placed in equilibrium. If the 205-N force acts in the +y-direction, what is one of the two configurations in the xy-plane that the remaining forces may have? Give numerical values for the angles. 275 N ° counterclockwise from the +x-axis 198 N ° counterclockwise from the +x-axis
The x-components of three vectors are Fx, +350 lbf, and -118 lbf. If they are in equilibrium, what is Fx.
Plunger (weightless) Area is 0.003 m² piston mass 1000 kg , area of piston is 0.3 m² density of oil is 750 kg/m³ determine force on Plunger required for equilibrium
A bored student builds a levitating lantern using objects they 3D printed in the Fischer Engineering Design Center. The student connects the blue and green pieces with two strings at points A and B, as shown below. If the blue (top) object weighs 181 g and the tension in string A is 3.2 N, what is the distance from the left side of the object to its center of mass in cm? Assume the system is in static equilibrium.
Explain: Equilibrium in two Dimension