A small block is attached to an ideal spring and is moving in SHM on a horizonta

Question

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m, it takes the block 2.48 s to travel from x = 0.090 m to x = -0.090 m.

Part A If the amplitude is doubled, to 0.180 m, how long does it take the block to travel from x = 0.180 m to x = -0.180 m? I have already answered this part as I know that if nothing changes except for the amplitude then the time doesn't change at all and therefore will remain 2.48 s.

Part B If the amplitude is doubled, to 0.180 m, how long does it take the block to travel from x = 0.090 m to x = -0.090 m?

I know that =2f, I know that f=1/t and that t in this case would be 2*2.48s. When I calculate I find that f=0.202Hz and so =1.27rad/s. Then when I use this all into the equation x=Acos(t + ) I have 0=0.18cos(1.27t - /4) and from here I plan to double my answer to get the total time that it takes. When I calculate my total I find that t=1.86 s. This answer didn't work for me so I found that someone else used 0.09=0.18sin(t) and so I did use it and it worked. However, what puzzles me is to why my equation earlier didn't work? I would think that since this is the position equation and since I managed to find all the necessary variables (or at least I think I did) that I should be able to solve it just using this equation. If I can solve using the first equation stated then please ellaborate as to where I made my mistake. If not, then please ellaborate as to the reason why it doesn't work and to the reason why the second one is the only one that would work.

Thanks in Advance

Explanation / Answer

part A) same. i.e 2.48 s

because time periode does not depend on mass of the body.

B) A = 0.18 m

T = 2*2.48 s

= 4.96 s

angular frequency, w = 2*pi/T

= 2*pi/4.96

= 1.267 rad/s

now, use

x = A*cos(w*t)

at t = t, x = 0.09 m

x = A*cos(w*t)

0.18 = 0.09*cos(w*t)

0.5 = cos(w*t)

cos(pi/3) = cos(w*t)

==> t = pi/(3*w)

= pi/(3*1.267)

= 0.8265 s

we know, time take from 0.18 to 0 = T/4

and time taken from 0 to -0.18 = T/4

so, time taken from 0.09 to -0.09 m = T/2 - 2*t

= 2.48 - 2*0.8265

= 0.827 s <<<<<<--------------------Answer

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