Question

A particle moves with SHM in a straight line. In first pi seconds after starting from rest it travels a distance a, and in the next pi seconds it travels 2a, in same direction, then what is the time period?

Answer 1

x=Asin(wt +phi) coz the particle starts from rest.. right?

Answer 2

The particle starts from rest, so it must be one of the extreme positions of the path, right? Choose initial phase accordingly.

Answer 3

oh! so x=Acos(wt +phi) is better?

Answer 4

Why do you have the "phi" there?

Answer 5

sry. x=Acos(wt)
and
a= Acos(pi *w)
2a= Acos (pi*w) or 3a= Acos(2pi *w)?

Answer 6

Initially, \(x = -A\) (you can choose +A too but I like left-to-right more).
\[A\sin ( \omega (0) + \phi) = -A\]\[\Rightarrow \phi = -\pi/2\]So\[x = A \sin (\omega t - \pi/2) = -A\cos {\omega t} \]Now\[-A + a = -A \cos \omega \pi\]\[-A + 2a = -A \cos \omega (2\pi)\]

Answer 7

Starting from right extreme looks simpler here

Answer 8

In that case, we'll have\[A - a = A \cos \omega \pi\]\[A - 2a = A \cos \omega (2\pi)\]Mostly the same.

Answer 9

can we continue will my eqs?

Answer 10

Oh, my equations are wrong

Answer 11

In that case, we'll have\[A - a = A \cos \omega \pi\]\[A - \color{red}{3 a} = A \cos \omega (2\pi)\]Mostly the same.

Answer 12

a= Acos(pi *w)
2a= Acos (pi*w) or 3a= Acos(2pi *w)? pls answer this