x Turn on thread page Beta
 You are Here: Home >< Maths

# STRINGS and shm watch

1. The question is:
------------------------------------------------------
A light elastic STRING on nat len 20cm and mod 40N has one end attached to a fixed point A on a smooth horizontal surface and a body of mass 2kg attached to the other end. The body is held on the surface at a point which is 40cm from A and released. Show that the subsequent motion will be PERIODIC and find the TIME PERIOD of the motion and the speed of the body as it passes through A.
--------------------------------------------------------------------------
Using Hooke's Law I found 100x = -x doubledot.

If it were a SPRING I would then say "therefore shm" but when it's a STRING do I say "therefore periodic"?

The answer for the time period is 0.2(2 + pi) secs and I have tried working out how come but can't. (But see later)

For the last bit I used vmax = aw and got 2. Because it's a string I suppose the mass just carries on at that speed?

oooo I've just had a thought. Does the mass wizz through A and then, being still attached to the string, go the distance of the string and its extension and then come back?

So it goes 0.8 m at 2m/s + time taken to stretch and recover (which I have been calling period of oscillation) = pi/5

I've tried it and the answer is as required but I don't know why the book has written it in that format.

So I suppose my questions are:

What the difference is SHM and PERIODIC MOTION or are they different words for the same thing one for springs and one for strings?

Are the words TIME PERIOD and PERIOD OF OSCILLATION interchangeable or are they used under different circumstances (strings and springs).

Finally what maths went into the book's method to come up with 0.2(2 + pi) rather than 0.4 + pi/5.

Thanks.
2. (Original post by maggiehodgson)

...

.
the motion described is periodic with SHM sections and motion with constant speed assuming no friction
(Springs will not do that)
3. (Original post by TeeEm)
the motion described is periodic with SHM sections and motion with constant speed assuming no friction
(Springs will not do that)
Super. That clears up the terminology perfectly. Thanks

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 16, 2016
Today on TSR

### How do I turn down a guy in a club?

What should I do?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams