10) Hooke's law is applicable to idealized (linear) springs that are not stretched or compressed too far. Consider a nonlinear spring whose restoring force is given by F(x) = 16x - 0.3x3, for Ixl s9. How much work is done in stretching the spring from its equilibrium position (x = 0) to x = 1? Round to two decimal places when appropriate.

a. Work of 4 Joules is done in stretching a spring from its natural length to 11 cm beyond its natural length. What is the spring constant k > 0? k = Don't forget to enter the correct units. b. If the spring is stretched to the same distance (11 cm), what is the restoring force that pulls the spring back toward its equilibrium position? Restoring force Don't forget to enter the correct units.

A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 16 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Useg = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft

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A 4 – foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to v2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 5 ft/s. Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?

A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a 1 damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s? for the acceleration due to gravity.) x(t) = ft

2. A mass of 4 pounds stretches a spring 0.4 feet. The mass moves through a medium which offers a damping force that is numerically twice the value of the instantaneous velocity. a) Find the equation of motion if the mass is released from rest 1 foot below the equilibrium position. b) Find the time the mass passes through the equilibrium position for the first time. Solve using algebraic techniques. л c) Find the velocity of the mass and direction (upwards or downwards) at /==sec. 4

A force of 13 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.6 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (b) Express the equation of motion in the form  (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)

5) PLEASE BE REALLY CLEAR WITH YOUR WRITTING AND EXPLANATION, IF POSSIBLE USE TEXT WRITING (KEYBOARD) IF NOT, AGAIN BE CLEAR, THANKS.

A mass weighing 16 pounds stretches a spring 8 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a 1 damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration 2 due to gravity.) x(t) = ft