When does the elastic string become slack in simple harmonic motion?

[markosheehan]

A particle of mass m is suspended from a point p on the ceiling by means of a light elastic string of natural length d and elastic constant of 49m/d. it is pulled down a distance 8d/5 below p and released from rest.
(i) show it will preform SHM as long as the string remains taut.
(ii) find in terms of d when the string becomes slack for the first time

i tried working this out by working out the forces up and down and finding the net force and equaling it to m by a but it would not work out. i have no idea how to work out the second part

 

[Joppy]

I'm sure you have already, but have you drawn a FBD? Knowing, and being able to see the unstretched position, static equlibrium position, and all the forces present will help tremendously in this situation :).

For motion to be harmonic, it must have no damping (neglecting internal damping), and have no external forces acting on it. Also, it must be periodic. That is, if $$f(t) = f(t + T)$$ for all t, then f(t) is said to be periodic.

Furthermore, we can express the position mathematically as,

$$x(t) = A\sin\left({\frac{2\pi}{T}t}\right)$$ where T is the period.​

Of course, taking the time-derivative of the above will yield the velocity and acceleration.

Is it possible to show us your working? That way we can get a gauge on what you are working with, and think is relevant to the question.

I know this isn't much help, but hopefully I've attracted some attention to your thread :p, and tonight when I'm free i'll try get around to solving it :).

 

[markosheehan]

i am not sure of your method, what i tryed to do was find the force down and the force up find the resultant force and let it equal to F=5a and then that would prove it but to do this when i am finding the force in the string i need the natural length of the string but it is not given in the question. to find the force up i use F=k(length-natural length)