A mock`-` up of a `CO_(2)` molecule consists of three balls interconnected by identical light springs and placed along a straight line in the state of equilibrium. Such a system can freely perform oscillation of two types, as shown by the arrows in figure. Knowing the masses of the atomes, find the ration of frequencies of these oscillations

Two cubes of mass m_(1) and m_(2) are interconnected by a weightless spring of stiffness k and placed on a smooth horizontal table. Then the cubes are drawn closer to each other and released. Find the frequency of oscillation.

A block of mass m is connected between two springs (constants K_(1) and K_(2) ) as shown in the figure and is made to oscillate, the frequency of oscillation of the system shall be-

Two identical springs S_(1) and S_(2) are joined as shown in the figure. The oscillation frequency of the mass m is v. What will be the frequency of mass m, if one spring is removed ?

As shown in the figure a block of mass m is hung from the ceiling by the system of springs consisting of two layers. The force constant of each of the springs is k. The frequency of the vertical oscillations of the block is

Two identical small discs each of mass m placed on a frictionless horizontal floor are connected with the help of a light spring of force constant k. The discs are also connected with two light rods each of length 2sqrt(2)m that are pivoted to a nail driven into the floor as shown as shown in the figure by a top view of the situation. If period of small oscillations of the system is 2pi sqrt((m//k)) , find relaxed length (in meters) of the spring.

Two balls with masses m_(1)=1.0 kg and m_(2)=2.0 kg are slipped on a thin smooth horizontal rod ( figure ) . The balls are interconnected by a light spring of stiffness x=24 N//m . The left- hand ball is imparted the initial velocity v_(1)=12 cm//s . Find : (a) the oscillation frequency of the system in the process of motion, (b) the energy and the amplitude of oscillations

Two cubes with masses m_(1) and m_(2) were interconnected by a weightless spring of stiffness x and placed on a smooth horizontal surface. Then the cubes were drawn closer to each other and released simultaneously. Find the natural oscillation frequency of the system.

A stepped pulley having mass m redius of gyration k is connected with two ideal springs of stiffnesws k_(1) and k_(2) as shown in figure. If the pulley shown in the figure . If the pulley rolls without sliding, find the angular frequency of its oscillation.