A rigid block of mass M is mounted on four elastic supports, as shown in the figure below. A small mass m drops from a height hand adheres to the rigid block without rebounding, and the spring constant of each elastic support is k. Determine the equation of motion of the system after the small mass strikes the block. Given the following values, if the equation of motion is in the form + az = 0, determine the value of a. M = 55 kg; m = 6 kg; k=181 N/m; h= 20 cm

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The mass m in the given figure is attached to a rigid lever with negligible mass and negligible friction in the pivot. The input is the displacement x. When x and θ are zero, the springs are at their free length. Assuming that θ is small, identify the equation of motion for θ with x as the input.

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Derive the equations of motion using Lagrange's equations. (I, =mr? ) THE MOTION IS ON THE HORIZONTAL PLANE (NO GRAVITY) Trailer, mass M Cylinder, k1 mass m k2

A block of mass m₁ is suspended from the ceiling with a spring k and damper b. Attached to the block is a massless rod of length L. Affixed to the end of the rod is a point-mass of mass m₂. Gravity is acting in the direction indicated in the figure. Use the energy method to set up the energy expression you would use to calculate the equations of motion for the system. Hint: be sure to decompose the velocity of the pendulum into horizontal and vertical components. DO NOT CALCULATE THE EQUATIONS OF MOTION, only setup the energy expression. x(t) b 7 m₁ e(t) (m₂

The following​ mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x1′​(0)=x2′​(0)=​0)in its equilibrium position (x1​'(0)=x2​'(0)=​0) with the given external forces F1​(t)=0and F2​(t)=540 cos 4t acting on the masses m1and m2​,respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies.   m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3   m1=​1, m2=2​; k1=1​, k2=2​, k3=2       Find the resulting motion of the system.   x1​(t) =   x2​(t) =   ​(Type exact​ answers, using radicals as​ needed.)

Learning Goal: Use the general equations of motion for plane motion to determine the initial acceleration of a spool. A spool has an outer radius R = 380 mm, an inner radius r = 210 mm, a mass m = 90 kg, and a radius of gyration KG = 320 mm. A rope is wrapped around the inner radius and pulled to the right as shown in (Figure 1). The coefficient of static friction between the spool and the ground is us = 0.2. The coefficient of kinetic friction is k = 0.15. Figure R A P 1 of 1 Part A Draw the free-body diagram for the spool, assuming the friction force acts to the right. Draw the vectors, starting at the black dots. The location and orientation of the vectors will be graded. The length of the vectors will not be graded. + 0 No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Submit Request Answer

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