## anonymous 4 years ago a particle starts SHM from the mean position. its amplitude is A and time is T.at what time when its speed is half of the maximum speed, its displacement is y is?

1. JamesJ

You mean its period is T?

2. anonymous

here i did v^2=A^2-X^2 and here we know max velocity is Aw=vmax w=2pie/T but nw i m unable to solve it further by keeping its value in the above formula

3. anonymous

A2pie/T=A^2-X^2 its complex ... am i doing sm mistake because its becoming complex means i had done some mistakes anywhere

4. JamesJ

Please clarify. T is the period of the system?

5. anonymous

yea

6. anonymous

hey for pie^2 we can take it approx 10 rit

7. anonymous

as its value is 3.14 so by squaring we can take approx 10??

8. JamesJ

Ok then. In which case the angular frequency $$\omega$$ is given by $\omega = \frac{2\pi}{T}$ and the equation of motion of the system is $x(t) = A \cos( \omega t + \phi)$ Now, to solve the problem, first find $$\phi$$ and then use this equation to find the value of $$t$$ for which $$v(t) = \dot{x}(t)$$ is half the maximum velocity, which you'll also want to find.

9. anonymous

how can we find phi will u plz solve dis ques i think i need a solution here to see where i m lacking

10. JamesJ

Look at the wording of the question and ask yourself what happens when t = 0.

11. anonymous

wait a min they are asking time t rit or displacement??

12. JamesJ

Both I think. This is where writing the question in clear English is so important.

13. anonymous

in my text they always write in a twisted form and i cant fight with education system alone to write it in good english :P

14. anonymous

hey i just rechecked the formula i used it was wrong the formula must be v^2=w^2A^2-A^2x^2 my mistake i got my ans now :P

15. JamesJ

To find phi: we're told that "a particle starts SHM from the mean position" hence x(t=0) = 0. But $x(0) = A \cos(0 + \phi)$ thus $$\cos \phi = 0$$ and therefore $$\phi = \pi/2$$. We can now write $x(t) = A\cos(\omega t + \phi) = A\sin(\omega t)$

16. anonymous

i got it i got it nw dont solve plz......

17. JamesJ

I'm solving from first principles. But I'll stop if you really want.

18. anonymous

yea plz actually if i see solution i dont use my mind dat is bad u cant help me in exam time dats y ...

19. JamesJ

I respect that.

20. anonymous

thanQ listen i m in confusion wid other i m nt able to make eaquation plz help me

21. anonymous