M4 Damped and Forced Harmonic OscillationsWatch

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Thread starter 4 years ago
#1
This is question 9 from Exercise 4A of the old Edexcel M4 Textbook:

A light spring , having natural length and modulus of elasticity , lies straight and at its natural length at rest on a horizontal table. A particle of mass is attached to the end .
The end is then moved in a straight line in the direction with constant speed . The resulting motion of the particle is resisted by a force of magnitude where is the speed of the particle. If is the extension of the spring at time , show that Obtain in terms of .

I have done the first part of the question have got an answer for the second part of the question of: , by using the initial conditions of , when .

However, the answer given in the book is which seems to have used an initial condition of when .

So, which initial condition is correct for this situation?
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4 years ago
#2
(Original post by JRichardson12)
This is question 9 from Exercise 4A of the old Edexcel M4 Textbook:

A light spring , having natural length and modulus of elasticity , lies straight and at its natural length at rest on a horizontal table. A particle of mass is attached to the end .
The end is then moved in a straight line in the direction with constant speed . The resulting motion of the particle is resisted by a force of magnitude where is the speed of the particle. If is the extension of the spring at time , show that Obtain in terms of .

I have done the first part of the question have got an answer for the second part of the question of: , by using the initial conditions of , when .

However, the answer given in the book is which seems to have used an initial condition of when .

So, which initial condition is correct for this situation?
Is it not just the dx/dt=V one ? Due to the information of a constant speed.

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Thread starter 4 years ago
#3
(Original post by physicsmaths)
Is it not just the dx/dt=V one ? Due to the information of a constant speed.

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There's an example in the new book that's very similar where they take :  But, then in the next question of the old book, they have another question where they have a initial condition equal to the constant speed.
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4 years ago
#4
(Original post by JRichardson12)
There's an example in the new book that's very similar where they take :  But, then in the next question of the old book, they have another question where they have a initial condition equal to the constant speed.
I have the book and i am currently working through M4 aswell,

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4 years ago
#5
(Original post by JRichardson12)
There's an example in the new book that's very similar where they take :  But, then in the next question of the old book, they have another question where they have a initial condition equal to the constant speed.
Which questions are you taking about ?

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Thread starter 4 years ago
#6
(Original post by physicsmaths)
Which questions are you taking about ?

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Ah, sorry. I meant to be clearer. I mean question 10 of Exercise 4A of the old book on page 99, with the original question in my first post being question 9 of Exercise 4A.

Also, I mean the example on page 86 of the new book in case that was also unclear.
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