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5 Modeling of Mechanical Oscillatory Systems …
Fig. 5.59 Angular velocity of the disks at gear ratios n = 3; 0.3; 1
5.8 Mechanical System with Two Springs and a Block
Formulation of the problem
Let the mechanical system consists of two ideal springs with individual stiffness k 1
and k 2 , fixed on independent suspensions, and an inextensible thread is attached to
the ends of the springs, on which the mass block m p is located. A block of mass m L
can be suspended from the block.
The positive directions of the linear velocities of the springs v 1 , v 2 , the vertical
speed of the block v 3 , and its angular velocity ω are shown in Fig. 5.61.
Tasks
It is necessary to study this system, making up equations describing the change in
the system over time, and build its computer model under various initial conditions.
Investigate the behavior of the system depending on the initial conditions themselves
and the way they are set.
Initial conditions: spring extension and block speeds v 3 and w are equal to zero,
k 1 = 5 N/m, k 2 = 10 N/m, m p = 0.5 kg, m L = 10 kg, R p = 0.3 m. Initial values of
state variables are set using start attribute.