Simple harmonic motion in a string

[aurao2003]

Homework Statement

Hi
I need some clarification on this question
A light elastic string of natural length 50 cm and modulus 20 N has one end fastened to O on a smooth horizontal table. The other end has a particle of mass 0.4 kg attached to it and the particle is released from rest at a distance 60 cm from O. Find the time it takes to reach O.

Homework Equations

The Attempt at a Solution

While the string is stretched
T=kx/l
=20x/0.5
=40x
40x=-.4a
So,a = -100x

w=10
T=2pi/10 =pi/5

I get stuck from here. Can anyone help please? Thanks

 

[ideasrule]

Think about how the mass moves after it's released. If the string were a spring, the mass would take a quarter of a cycle to return to its natural length, another 1/4 cycle to get to its farthest point, and 1/2 cycle to come back.

However, this is a string, which means it can't resist any compression. The mass would take 1/4 cycle for the string to return to its natural length. After that, the mass moves unimpeded all the way to O and beyond.

 

[aurao2003]

Thanks a lot guys! Sorry for late reply.