Amass moves back and forth in simple harmonic motion with amplitude a and period t.
(a) in terms of a, through what distance does the mass move in the time t? (b) through what distance does it move in the time 5.00t? (c) in terms of t, how long does it take for the mass to move through a total distance of 2a? (d) how long does it take for the mass to move through a total distance of 7a? (e) if the objects undergoes simple harmonic motion with a period t. in the time 5t/2 the object moves through a total distance of 16d. in terms of d, what is the object's amplitude of motion?

(a) 4A

In a simple harmonic motion:

- The amplitude is the maximum displacement of the system from the equilibrium position

- The period is the time that the system takes to make one complete oscillation: for example, the time it takes to go from a displacement of x=+A to the next x=+A.

So we have that the total distance covered by the system in one period T is 4 times the amplitude: 4A, because in one cycle the system does the following:

- Moves from x=+A to x=0 (equilibrium position) --> distance covered: A

- Moves from x=0 to x=-A --> distance covered so far: A+A=2A

- Moves from x=-A to x=0 (equilibrium position) --> distance covered so far: 2A+A=3A

- Moves from x=0 to x=+a --> distance covered so far: 3A+A=4A

(b) 20 A

We said that in a time of 1.0 T the system moves through a distance of 4A. Therefore, to find the distance d through which the system moves during a time of 5.0 T, we have to solve the following proportion:

So, it moves through a distance of 20 A.

(c) 0.5 T

We said that in a time of 1.0 T the system moves through a distance of 4A. Therefore, to find the time t that it takes for the mass to move a total distance of 2A, we have to solve the following proportion:

so, it takes half period.

(d) 1.75 T

We said that in a time of 1.0 T the system moves through a distance of 4A. Therefore, to find the time t that it takes for the mass to move a total distance of 7A, we have to solve the following proportion:

so, it takes 1.75 T.

(e)

We said that in a time of 1.0 T the system moves through a distance of 4A. So, the distance covered in a time of 5T/2 is given by the following proportion

The problem also says us that distance is equal to

d = 16 D

So by combining the two equations, we find

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

the following is queen elizabeth’s purposes:

- to encourage the parliament that the technique of picking successors to the seat based merely on birthright needs to be reviewed.

- (not) to convince the parliament that her kid should not be measured as a likely choice for heir to the english power.

- to persuade the parliament that merely since she has a child does not assure that the kid will be a capable leader.

- to sway the parliament how shattering it could be if they proceeded discourteously concerning her or her child.