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?