Question

1. 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 are the period and the amplitude of the function?
(d) What is the graph’s frequency and what does it indicate in this situation?
(e) How is the weight moving during the time period x = 4 to x = 5?

Answer 1

As, on the graph the y-axis shows the vertical displacement(in cm) and on x-axis the time is shown for weight attached to spring.
And this is the sine graph with zero vertical shift and zero horizontal shift.
(a)
You can see this directly from the sine graph that maximum displacement is the height from center line to either peak(crust or  the trough) so weight covers a maximum displacement of 10 cm.
(b)
As on the x-axis of sine graph, the time covered by the bouncing weight is shown,
 so when the weight is bouncing in one direction means( from its resting position to its extreme)  it covers 0.5 s and when the weight is bouncing again in other direction( means from that extreme to its resting position) than it again covers 0.5 s, so the total time is t=0.5+0.5=1 s
(c)
First, we find the frequency which is the no. of cycles in one second.
As in one second half of the cycle of graph is covered, so frequency is 1/2
and then the period is T=1/f 
So, T=2
and the amplitude is the maximum displacement which is 10.
(d)
Frequency which is the no. of cycles in one second.
As in one second half of the cycle of graph is covered, so frequency is 1/2.
(e)
During the time period from x=4 to x=5, the weight first moving in the upward direction towards its extreme(x=4 to 4.5) and then from that extreme it will move in the downward direction towards its resting position(x=4.5 to 5).