Math Is Fun Forum

markosheehan

Member

Registered: 2016-06-15

Posts: 51

shm

A particle of mass 5 kg is suspended from a fixed point by a light elastic stringwhich hangs vertically. The elastic constant of the string is 500 N/m.The mass is pulled down a vertical distance of 20 cm from the equilibriumposition and is then released from rest.(i) Show that the particle moves with simple harmonic motion.

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)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: shm

By natural length do you mean unstretched length or stretch due to weight of the body? Both are accounted for already.

  20 cm is over and above this.
You can start with

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: shm

hi markosheehan

You need to use the extension rather than the natural length.  The 'restoring' force is proportional to the extension but in the opposite direction so that gives you an equation like this:

That is the defining equation for SHM.  I think, but you'll need to check me on this, that k = 500.

I notice that this is just part (i)  If the subsequent parts involve velocities, positions and times, I expect I can do these too.   

(Used to be my favourite equation until I discovered this:

)

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob