This page addressess the analytical solution of text-books in the field of Strength of Materials, Solid Mechanics, Engineering Mechanics, Mechanical Vibrations, Kinematics & Dynamics of Mechanisms and Machinery...
This type of situation is very frequently encountered while solving statics and dynamics problems. What is the angle made by normal reaction with inclined plane or what is the component of gravity force perpendicular to the inclined plane? Just remember the theorem: "The angle between two lines is equal to angle between perpendicular to those lines".
Lagrangian approach is a powerful and straightforward method to derive equation of motion (EOM) for complex systems. The EOM for pring-mass-damper pendulum (also known as "sprung pendulum") is described below.
Collision is based on conservation of momentum and loss of energy defined by coefficient of restitution. This solution describes a case where one of the colliding objects is attached to a spring.
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