The following information pertains to questions 1-8.

Each force in the list of forces that make up this series of questions is the net, external force acting on an object of mass m_o that is free to move in the x direction only. The vector x is the displacement of the object relative to a fixed point on the x axis (this could be the origin). The symbols a, b, c and d are positive constants and F_o is a small constant force directed in the positive x direction. The proposition (True, T or False, F) is that each of these forces would cause the object on which it is acting to undergo simple harmonic motion.

F = a x

F = - d x

F = - (a x + F_o )

F = ((a + b + c)) x

F = - a x + F_o

F = - (b e^(c/d)) x

F = - ((a + b/d + c)) x

F = - a x /((x^•x))

The following information pertains to questions 9-17.

An object with mass m_o, free to move on a one dimensional, horizontal frictionless surface is subjected to a restoring force of magnitude k_ox where x is the distance separating the object from its equilibrium position, i. e., the position is which the net force acting on it is zero. The direction of this restoring force acting on the object is such that it always pushes or pulls the object back toward its equilibrium position. The object is pulled aside until it is a distance A_o from its equilibrium position, held at rest and released. The object then undergoes simple harmonic motion with period T_o. The total mechanical energy associated with the motion of the object is E_o. As the object passes through its equilibrium position its speed is v_o.

If the spring constant, k_o, had been slightly larger, the speed of the object as it passed through its equilibrium position would have been ___ v_o.

If the spring constant, k_o, had been slightly smaller, the period of the motion would have been ___ T_o.

If the spring constant, k_o, had been slightly larger, the total mechanical energy associated with the motion of the object would have been ___ E_o.

If the object had been released from rest at a distance less than A_o from its equilibrium position, the speed of the object as it passed through its equilibrium position would have been ___ v_o.

If the object had been released from rest at a distance greater than A_o from its equilibrium position, the period of the motion would have been ___ T_o.

If the object had been released from rest at a distance less than A_o from its equilibrium position, the total mechanical energy of the motion would have been ___ E_o.

If the mass of the object had been slightly less than m_o, the speed of the object as it passed through its equilibrium position would have been ___ v_o.

If the mass of the object had been slightly larger than m_o, the period of the motion would have been ___ T_o.

If the mass of the object had been slightly less than m_o, the total mechanical energy of the motion would have been ___ E_o.

The following information pertains to questions 18-29.

A simple pendulum is made by tying an object with mass m_o to the end of a string of length L_o, the other end of which is tied to the ceiling. The object is pulled aside until the string makes a small angle _o with the vertical, held at rest and released. The pendulum bob then undergoes simple harmonic motion with period T_o and the total mechanical energy of the pendulum bob is E_o. At the lowest point in its swing, the speed of the pendulum bob is v_o.

If the length of the string had been slightly longer than L_o, the period of the motion would have been ____ T_o.

If the mass of the pendulum bob had been slightly larger than m_o, the period of the motion would have been ____ T_o.

If the angle which the string makes with the vertical when the bob was released from rest had been slightly less than _o, the period of the motion would have been ____ T_o.

If the same pendulum was set in motion in the same way on the surface of the moon, the period of the motion would be ___ T_o.

If the length of the string had been slightly longer than L_o, the total mechanical energy of the pendulum bob would have been ___ E_o.

If the mass of the pendulum bob had been slightly larger than m_o, the total mechanical energy of the pendulum bob would have been ___ E_o.

If the angle which the string makes with the vertical when the bob was released from rest had been slightly less than _o, the total mechanical energy of the pendulum bob would have been ___ E_o.

If the same pendulum was set in motion in the same way on the surface of the moon, the total mechanical energy of the pendulum bob would have been ___ E_o.

If the length of the string had been slightly longer than L_o, the speed of the pendulum bob as it passed through the lowest point in its swing would have been ___ v_o.

If the mass of the pendulum bob had been slightly larger than m_o, the speed of the pendulum bob as it passed through the lowest point in its swing would have been ___ v_o.

If the angle which the string makes with the vertical when the bob was released from rest had been slightly less than _o, the speed of the pendulum bob as it passed through the lowest point in its swing would have been ___ v_o.

If the same pendulum was set in motion in the same way on the surface of the moon, the speed of the pendulum bob as it passed through the lowest point in its swing would be ___ v_o.