Question

The displacement x metres of an object from an origin O is given by x = A cos kt where A and k are constants. Prove that the object is initially at an extreme position. please show full working out.

Answer 1

@ujjwal

Answer 2

@moongazer

Answer 3

@amistre64

Answer 4

is this a roll call?

Answer 5

whats a roll call ?

Answer 6

its where you sit there at the beginning of class, and the teacher calls the roll to see who is here and who aint

Answer 7

what is the subject that this question comes from?

Answer 8

u are here~ :D

Answer 9

Calculus

Answer 10

Topic is Simple Harmonic Motion.

Answer 11

how are we to define "initially" and "extreme postition"?

the equation given is a generic setup for the cosine function having a nonspecific amplitude and nonspecific period

Answer 12

i assume t stands for time, and does initially refer to time zero?

Answer 13

If so, I would take the derivative, and apply t=0 to it to see if we get a derivative that equals zero

Answer 14

x = A cos (kt)

x' = -Ak sin(kt) ; at t=0, sin(0) = 0 tells us that we are at one extreme or the other

Answer 15

The answer is on question 24(a) the second part where it says RHS = LHs something like that, was wondering if u could dexplain to me that one. I understand ur way.

Answer 16

i can read thru the proof, but i got no idea why they did that :)

cos0=1, therefore A cos0 = A; RHS

Answer 17

from the first line on top, x = A cos kt; therefore LHS = |A cos kt|

Answer 18

well maximum acceleration is at the extremes

so they differentiated twice

Answer 19

|cos kt| alone ranges between 0 and 1, or rather

|cos kt| <= 1 ; multiply both sides by |A|

Answer 20

after replacing equals for equals; they get:

|A cos kt| <= |A|
LHS <= RHS

Answer 21

Since at x=0, we are already at |A|; and at every other point of "t" we are either less than or equal to |A| ....

Answer 22

and by x=0, i mean t=0 ;)