Spring Motion: 1-kg mass on spring w/ 16kg/sec^2 constant

[charlesmci]

Hi, I've been given this question and have no idea where to start. Any help would be appreciated.

Question 2: A 1-kilogram mass is attached to a spring whose constant is 16 kg/second/second, and the entire
system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the
instantaneous velocity. Determine the equations of motion if

(a) the mass is initially released from rest from a point 1 meter below the equilibrium position, or
(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward
velocity of 12 m/s.

In parts (a) and (b) determine whether the mass passes through the equilibrium position. In each case
find the time at which the mass attains its extreme displacement from the equilibrium position. What
is the position of the mass at this instant?

 

[Deleted member 4993]

Re: Spring Motion

Hi, I've been given this question and have no idea where to start. Any help would be appreciated.

Question 2
A 1-kilogram mass is attached to a spring whose constant is 16 kg/second/second, and the entire
system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the
instantaneous velocity. Determine the equations of motion if
(a) the mass is initially released from rest from a point 1 meter below the equilibrium position, or
(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward
velocity of 12 m/s.
In parts (a) and (b) determine whether the mass passes through the equilibrium position. In each case
find the time at which the mass attains its extreme displacement from the equilibrium position. What
is the position of the mass at this instant?

Do you know the physics behind this problem? We cannot teach you the WHOLE thing here. Start by reviewing at:

http://en.wikipedia.org/wiki/Harmonic_oscillator

 

[charlesmci]

I think I have a reasonable understanding of the physics of the situation it's mainly putting it into a DE that's confusing me. We've been given the formula:
y'' + (c/m)y' + (k/m)y = 0 for damped oscillatory motion but I'm confused as to what goes where; in particular how to include the criteria in part (a) that the mass is released from rest 1 meter below the equilibrium position? Is that forming an Initial Value Problem or how do I use that information?

 

[Deleted member 4993]

I think I have a reasonable understanding of the physics of the situation it's mainly putting it into a DE that's confusing me. We've been given the formula:

y'' + (c/m)y' + (k/m)y = 0 <<< Correct

for damped oscillatory motion but I'm confused as to what goes where; in particular how to include the criteria in part

(a) that the mass is released from rest <<< y'(0) = 0

1 meter below the equilibrium position? <<< y(0) = -1

Is that forming an Initial Value Problem <<< Yes - you are given initial conditions (at t = 0)

or how do I use that information? <<< Discussed above

 

[charlesmci]

Thank you!