Particle executing SHM

1. Feb 20, 2015

Saurav.1905

1. The problem statement, all variables and given/known data
For a Particle executing SHM, the displacement x of the particle as a function of time is given as x=A sin 2 pi t, where x is in cm and t is in seconds. Let the time taken by the particle to travel from x = 0 to x =A/2 be t1 and the time taken to travel from x=A/2 to x = A be t2.
Find the ration of t1/t2

2. Relevant equations

3. The attempt at a solution
t1/t2...

t1 = (x * 2)/(A sin 2 pi)
t2 = (x *2) /(A sin 2 pi)

as Total distance is A...
In t1 cover A/2 ( Half distance)
So in t2 also cover A/2 ( remaining half)

Last edited: Feb 20, 2015
2. Feb 20, 2015

Saurav.1905

3. Feb 20, 2015

Jediknight

it will be at A/2 when sin(2pit)=1/2 so 2pit=pi/6 (unit circle)

so what does t equal at that time, what does 2pi t have to equal for x to be A? what does t equal to make these true (just algebra there)

relevant equations
x=Asin(ωt) as you stated ω=2pi

Δt=t(final)-t(initial)

the concept is more quantitive than qualitive, the point here to notice is that even though velocity acceleration and position are always changing, the fack that F=-kx with shm allows you to derrive an amazing amount of information based on the trig patterns they follow and those patterns simple relation to thier derivatives. The range of quantitive information you can gather from so little given using the trig functions is the concept

Last edited: Feb 20, 2015
4. Feb 20, 2015

Saurav.1905

Thanks Jediknight....