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 \(\displaystyle f(t) = f(t + T)\) for all t, then f(t) is said to be periodic.

Furthermore, we can express the position mathematically as,

\(\displaystyle x(t) = A\sin\left({\frac{2\pi}{T}t}\right)\) 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)