A single mass m1 = 4.6 kg hangs from a spring in a motionless elevator. The spring is extended x = 10.0 cm from its unstretched length.1) What is the spring constant of the spring?2) Now, three masses m1 = 4.6 kg, m2 = 13.8 kg and m3 = 9.2 kg hang from three identical springs in a motionless elevator.
Problem15‐13: In the figure two springs of spring constant k l and k r are attached to a block of mass m. Find the frequency and period. k l k r Let the positive x be to the right then the force on the block at x is: −(xk l +xxkkr)=mmaa a=− ()xk l +xk r m =−ω2a f =2πω T = 1 f A two degree-of-freedom system (consisting of two identical masses connected by three identical springs) has two natural modes, each with a separate resonance frequency. The first natural mode of oscillation occurs at a frequency of ω=(s/m) 1/2 , which is the same frequency as the one mass, one spring system shown at the top of this page. s1 = m. spring (k=1500000, l=0, m1=m1, m2=m2, color= (255, 0, 0), visible=True)
A system of masses connected by springs is a classical system with several degrees of freedom. For example, a system consisting of two masses and three springs has two degrees of freedom. You have two equal masses m1 and m2 and a spring with a spring constant k. The mass m1 is connected to the spring and placed on a frictionless horizontal surface at the relaxed position of the spring. You then hang mass m2, connected to mass m1 by a massless cord, over a pulley at the edge of the horizontal surface.