Lesson Worksheet: Free and Forced Oscillations Physics • 9th Grade

The graphs show the changes in displacement with time of a simple harmonic oscillator that dissipates energy as it oscillates freely. Which line corresponds to the oscillator under the condition of critical damping?

A horizontal spring is mounted on a wall, as shown in the diagram. The end of the spring not attached to the wall is connected to a solid board. A pendulum of length is suspended vertically from a platform near the spring. The board is initially at the point , which corresponds to the equilibrium position of the spring. The spring is displaced a distance and then released. The recoiling spring pushes the board into the pendulum bob, setting the pendulum into simple harmonic motion. The value of is varied by raising or lowering the platform from which the pendulum is suspended, ensuring that the pendulum bob always collides with the center of the board. The amplitude of the oscillation of the pendulum for different values of is measured until a value of is determined for which the amplitude is greatest. For this value of , which of the following correctly relates , the natural frequency of the spring, to , the natural frequency of the pendulum?

A horizontal spring is mounted on a wall, as shown in the diagram. The spring has a natural frequency of 55 Hz. A solid board covers the end of the spring opposite to the end of the spring attached to the wall. A loudspeaker that oscillates at 250 Hz vibrates the air particles between itself and the board attached to the spring. Which of the following frequencies is closest to the frequency at which the spring will oscillate?

A system is displaced from equilibrium. The displacement of the system produces a restoring force that acts toward the equilibrium position of the system. No other forces act on the system apart from the restoring force. Which of the following is the correct term for the frequency at which the system oscillates?

A rod has a pendulum connected to each of its ends, as shown in the diagram. An external force is continuously applied to the smaller pendulum that causes it to oscillate at its natural frequency, . After some time, the larger pendulum oscillates. Which of the following correctly describes the frequency of the forced oscillations of the larger pendulum?

Two horizontal springs with negligible mass are mounted on walls, as shown in the diagram. The ends of each spring not connected to a wall are connected to opposite faces of a solid board of mass . The board is initially at the point , which corresponds to the equilibrium position of the system of springs. The system is displaced a distance by an applied force and then released. Which of the following correctly describes how the restoring forces of the springs produce oscillation of the system?

The graph shows how the amplitude of the oscillation of a system changes with the frequency at which the system is forced to oscillate. Which of the frequencies , , or is the natural frequency of the system?

In which of the graphs shown does the green line represent the change in the resonance characteristics of an oscillating system for which damping is increased from the amount of damping that produces oscillations represented by the black line?