# M3 edexcel simple harmonic motion

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#1
Can someone help me with part c to an example question from M3 edexcel (Keith Pledger):

A particle P of mass 0.69 kg rests on a smooth horizontal floor attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 16N. The other end of the string is fixed to a point A on the floor. The particle is pulled away from A until AP measures 1.2m and released.
c) calculate the time that elapses between the point where the string becomes slack and the point where it next becomes taut.
d)Calculate the time taken by the particle to return to its starting point for the first time.

the period of the S.H.M is found to be 1.088s
and the time taken for part (c) is 0.693s
when working out the total time they have written : 1.088...+2 x 0.693 = 2.473..
Why have they multiplied 0.693 by 2?
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6 years ago
#2
(Original post by triciapat9)
Why have they multiplied 0.693 by 2?
I persume you mean part d, rather than c.

If I interpret correctly from what you've written:

For a complete cycle from release the particle travels, whilst slack, from one side of A to the other and then back again hence 2 times 0.693.
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#3
Thank you for your reply.Sorry, yes, part d . doesn't the string in part c become taut when it's stretched past its natural length ? So it would already have ready travelled from one side of A to the other and back again? or am I mistaken :/
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6 years ago
#4
(Original post by triciapat9)
Thank you for your reply.Sorry, yes, part d . doesn't the string in part c become taut when it's stretched past its natural length ?
Yes.

So it would already have ready travelled from one side of A to the other and back again? or am I mistaken :/
Initially, prior to release, the particle is pulled to one side (I'll call it the left side for ease of description) beyond its natural length and the string is taut.

It's released.

It travels from the left side, initially string taut, then slack and over to the right, initially with string slack, and then taut (that's half a cycle)

It gradually comes to instantaneous rest, and then reverses its path, performing the same movements in reverse (doing another half cycle), back to its starting point having completed one whole cycle.

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#5
It travels from the left side, initially string taut, then slack and over to the right, initially with string slack, and then taut (that's half a cycle)

I'm sorry I'm just confused about why it becomes taut again on the right side too? It's compressed up to the fixed point A on the floor ? Isn't it slack when compressed ?
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6 years ago
#6
(Original post by triciapat9)
It travels from the left side, initially string taut, then slack and over to the right, initially with string slack, and then taut (that's half a cycle)

I'm sorry I'm just confused about why it becomes taut again on the right side too? It's compressed up to the fixed point A on the floor ? Isn't it slack when compressed ?
It's a string. It doesn't get compressed, just slack. Think of it as a yoyo on an elastic string.

You may be confusing this with the idea of a spring which would cause oscillations on just one side of A, and never reach A at all.
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#7
(Original post by ghostwalker)
It's a string. It doesn't get compressed, just slack. Think of it as a yoyo on an elastic string.

You may be confusing this with the idea of a spring which would cause oscillations on just one side of A, and never reach A at all.
Ooh, omg thank you so much, I was confusing it for a spring.
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