Question

2. The graph shows the vertical displacement y, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds, x.

(a) What is the weight’s maximum displacement?
(b) From its resting position, how long does it take the weight to bounce one direction, then the other, and then return to its resting position?
(c) What is the graph’s frequency and what does it indicate in this situation?
(d) How is the weight moving during the time period x = 4.5 to x = 6?

Answer 1

(a) The weight's maximum displacement is 14 centimeters, given by the amplitude of the graph. (b) The time for one complete cycle is the period. Locate the first positive and negative peaks to find it. (c) The graph's frequency is the reciprocal of the period, indicating the number of cycles per unit of time. (d) The weight is moving upward from x = 4.5 to x = 6, completing one-half of a cycle in that time period.

(a) The weight's maximum displacement is the amplitude of the graph, which is given as 14 centimeters.

(b) To find the time for one complete cycle (bounce in one direction, then the other, and back to the resting position), look for the first positive and negative peaks on the graph. This duration is the period of the oscillation.

(c) The graph's frequency can be determined by calculating the reciprocal of the period. Frequency = 1 / Period. It indicates how many complete cycles occur per unit of time.

(d) The weight is moving upward and reaches its peak during the time period x = 4.5 to x = 6, indicating one-half of a complete cycle.