hello friends,

 

i have one problem regarding occilation topic.i am posting problem defination pls provide me the solution as soon as possible.

 

Que:the Displacement of a particle in Simple harmonic motion is given by

 

x = 8sin(5pie*t + pie/6),

where time is in seconds and displacement in meter .

 

Find 1)displacement 2)velocity 3)Acceleration,

of a particle at t=2 sec.

 

 

 

Thanks and Regardrs,

rahul.

1) This is homework so you should probably have posted the question in the homework section.

2) There you might have read that it is not the idea of this forum to give solutions but only to help the people at finding the solution themselves.

3) Also, you might have read that you should state what you already tried and did yourself.

3a) You are given a function x(t)=... for the displacement x for each time t. Do you think you are able to find the displacement x at some given time t=2 from that?

3b) How are velocity and acceleration related to the displacement/position? Start with the velocity: What is the definition of velocity? Can you apply this definition to the only information you were given, the function x(t)=.... ?

 

Btw: The greek letter [math]\, \pi[/math] is written "pi", not "pie". But that does not matter for your question, of course.

what is the period T of system?

the Displacement of a particle in Simple harmonic motion is given by

 

[imath]x(t) = 8 \sin(5\pi t + \frac{1}{6}\pi)[/imath],

where time is in seconds and displacement in meter .

 

Find 1)displacement 2)velocity 3)Acceleration,

of a particle at t=2 sec.

Since you already have a formula for displacement, you can just evaluate it at t=2. Recall that velocity and acceleration are the first and second derivatives of displacement, respectively. From there you will have formulae which again, simply need to be evaluated at t=2

 

what is the period T of system?

What on earth does that have to do with anything?

we should know the periodu other wise we cant know the answer.

we should know the periodu other wise we cant know the answer.

Sure we can.

 

Sorry to push at the rules (I'm assuming the deadline has been passed) but the answers as calculated according to the definitions as I said in my previous post:

 

[hide]displacement: x(t)|_t=2 = 8.sin(61.pi/6) = 4

 

velocity: d²x(t)/dt²|_t=2 = 40.pi.cos(61.pi/6) = 20.sqrt(3).pi

 

acceleration: d³x(t)/dt³|_t=2 = -200.pi².sin(61.pi/6) = -100.pi²[/hide]

 

Clearly, there's no need to know what the period of the function is, that it is oscillating, that it is un-dampened, what it's amplitude is - or even what any of those words mean in order to answer the question as presented.