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mass and spring question

stuck on part b:
Attachment not found


This is my working: Screenshot_2015-11-30-14-28-00.jpg

Is it right? if it's wrong, what should I do instead?

and is c just a straight line starting from 0, going diagonally from left to "high" right?
(edited 8 years ago)
20151130_142217.jpg526.0KB
Original post by Airess3
stuck on part b:
Attachment not found


This is my working: Screenshot_2015-11-30-14-28-00.jpg

Is it right? if it's wrong, what should I do instead?

and is c just a straight line starting from 0, going diagonally from left to "high" right?


You've got the wrong DE, think about the net force on the mass and then use F=mx''

Spoiler



For (c), think about what would happen to a mass on a spring with friction (you might want to try this a model mass). What you're saying implies the magnitude of the oscillation will increase without bound, but this definitely isn't be case. How does your solution relate to the ideal SHM model without friction?
(edited 8 years ago)
Original post by silentshadows
You've got the wrong DE, think about the net force on the mass and then use F=mx''

Spoiler



For (c), think about what would happen to a mass on a spring with friction (you might want to try this a model mass). What you're saying implies the magnitude of the oscillation will increase without bound, but this definitely isn't be case. How does your solution relate to the ideal SHM model without friction?


Thanks! This is my re-working, I did a bit of an alternative: Screenshot_2015-12-01-22-35-14.jpg and this is for c):
Attachment not found


a mass on a spring with friction would bounce up and down repeatedly if it was hung from the ceiling? Does the graph look something like a cosine?

And I'm stuck on the 2nd explain part of the question for d):
Attachment not found


So far I've written: The arbitrary constants a and b are determined by the initial position and initial velocity of the mass.
Screenshot_2015-12-01-22-37-46.jpg164.3KB
20151201_224042.jpg505.3KB
Original post by Airess3
Thanks! This is my re-working, I did a bit of an alternative: Screenshot_2015-12-01-22-35-14.jpg and this is for c):
Attachment not found


a mass on a spring with friction would bounce up and down repeatedly if it was hung from the ceiling? Does the graph look something like a cosine?

And I'm stuck on the 2nd explain part of the question for d):
Attachment not found


So far I've written: The arbitrary constants a and b are determined by the initial position and initial velocity of the mass.


I can't see your pic for (c), but you're nearly there with the cosine idea. Think about what the effects of friction on the graph would be

Spoiler




I'm not sure how much detail you need for (d), but γ\gamma can be thought of as a damping coefficient and ω0\omega_0 can be thought of as a natural frequency for the system.

If you have some time, you might want to check out this video for a more detailed description of damped SHM: https://youtu.be/Zz-9UVpYcJI

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