How Far Will the Weight Drop When a 12 lb Weight is Added to a Stretched Spring?

[hatsu27]

Homework Statement

A spring is such that it would be stretched 3 in. by a 6 lb. weight. Let the spring first be stretched 4 ins. and then a 12 lb. weight attatched and given an initial velocity of 8 ft/s find out how far the wight will drop.

Homework Equations

d²y/dx²+(k/w)y=o

The Attempt at a Solution

I can't figure out exactly what they r asking me here- do I get my k from the first sentence making k=24 and w=3/8 and use the the others as
y(0)=1/3 and y'(0)=8, or are they asking me to use the 2nd weight and add it to the first and if so, how? is that an added force? I am really confused be the wording of this problem.

 

[tiny-tim]

welcome to pf!

hi hatsu27! welcome to pf!

A spring is such that it would be stretched 3 in. by a 6 lb. weight. Let the spring first be stretched 4 ins. and then a 12 lb. weight attatched and given an initial velocity of 8 ft/s find out how far the wight will drop.

… do I get my k from the first sentence making k=24 and w=3/8 and use the the others as
y(0)=1/3 and y'(0)=8, or are they asking me to use the 2nd weight and add it to the first and if so, how? is that an added force?

the clue is in the word "would" …

it hasn't been stretched by a 6 lb. weight, but if it was, it would stretch 3 in

so you only use that information to find k ​

 

[hatsu27]

Ok from there I got my diferential eq. y" + 64 = 0 so my x(t) = c₁cos(8t)+c₂sin(8t) and from there my sinusoidal is ((sqrt10)/3)cos(8t+tan^-1(3)) So to find out how far the wieght would drop i take the derivative and set it = to zero and solve for t yes? Does all this look good to u?

 

[tiny-tim]

Ok from there I got my diferential eq. …

why so complicated?

just use conservation of energy! ​

 

[hatsu27]

not allowed-only allowed to use tools learned in my dif eq. class. we are specifically told to not use physics formulas

 

[tiny-tim]

ohhh!

Ok from there I got my diferential eq. y" + 64 = 0 so my x(t) = c₁cos(8t)+c₂sin(8t) and from there my sinusoidal is ((sqrt10)/3)cos(8t+tan^-1(3)) So to find out how far the wieght would drop i take the derivative and set it = to zero and solve for t yes? Does all this look good to u?

the method looks ok (i haven't checked the figures)

though i don't think you'll have to find t, you may be able to read the answer off without that

(btw, you haven't said what units you're using )

 

[Bohrok]

The amplitude of cos is (√10)/3, so that should be how far the weight will drop in inches, if everything else is correct.