Define the equilibrium point of a dynamical system. Show that isolated equilibrium points may exist for a nonlinear system by considering the example of a pendulum

If a force of 20N is applied to the same spring and the total length of the spring is 200mm, what is the length of the relaxed spring with no force applied? (in units of m)

Please answer the question correctly

A spring-mass system shown in the diagram below is free to oscillate in the vertical direction. I+s unstretched x0 motion The position (x) of the spring is positive when the spring is below the equilibrium position. If the block is displaced from its equilibrium position by a distance x, show that its equation of motion is given by: K m Why is it that the equation of motion does not include the force of gravity? In which direction does the velocity of the moving mass have a positive value?

A protein dimer can be viewed as a dumbbell linked by a spring. Stretching of the spring with an AFM cantilever adds the total (internal) energy of 10−17 J to the dimer. What is the average kinetic energy of dumbbell oscillations after the external force has been released? Help me

A mathematical pendulum swings with angular amplitude α (α ≪ 1), its period is T . By what factor does the period of the pendulum change if it is suddenly surrounded by two perfectly elastic walls (see figure)? The walls are arranged symmetrically, their angular distance is α.

In this limit, what is the effective spring constant k for the pendulum in the limit of small angles? In this limit, what is the effective angular frequency ω of a pendulum in the limit of small angles?

A stiff spring k = 666 N/m has be attached to the floor vertically. A mass of 6.66 kg is placed on top of the spring as shown below and it finds a new equilibrium point. If the block is pressed downward and released it oscillates. If the compression is too big, however, the block will lose contact with the spring at the maximum vertical extension. Draw a free body diagram and find that extension at which the block loses contact with the spring.

A car with a mass  m = 1000.0kg  is moving on a horizontal surface with a speed  v = 20.0m/s  when it strikes a horizontal coiled spring and is brought to rest when the spring is compressed by a distance  d = 3.0m.  Calculate the spring stiffness constant  k  by...  (a) select appropriate common equations and make appropriate substitutions that are specific to the problem, and algebraically manipulate the equations to end with an algebraic expression for the variable the problem is asking you to solve for. (b) Show the numeric substitution of given quantities and show the final numeric result. (c) Draw a free body diagram for the system and define the given quantities.

A pendulum has length 94 centimeters and bob mass 700 grams and is dropped from an angle of 31 degrees from the vertical. b. We can treat the pendulum as a mass on a spring on a horizontal surface with an effective spring constant of (w/L), oscillating back and forth with an amplitude equal to the maximum horizontal distance from the equilibrium position. Using the law of conservation of mechanical energy and considering only kinetic energy and elastic potential energy, what is the maximum speed of the bob? Include units in your answer.   PLEASE ANSWER IN HANDWRITINGTHE SECOND PART OF THE ANSWER IS WRONG!!!! IT IS NOT 2.66 m/s