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

• hatsu27
In summary, the problem involves a spring stretched by different weights and an initial velocity. The goal is to find out how far the weight will drop using only tools learned in a differential equations class. The solution involves using conservation of energy and solving a differential equation, resulting in a sinusoidal function. The amplitude of this function, (√10)/3, represents the distance the weight will drop in inches.
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.

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.

welcome to pf!

hi hatsu27! welcome to pf!
hatsu27 said:
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

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?

hatsu27 said:
Ok from there I got my diferential eq. …

why so complicated?

just use conservation of energy!

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

ohhh!
hatsu27 said:
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 )

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

## 1. What is an oscillation in terms of spring motion?

An oscillation refers to the repetitive back and forth motion of a spring as it returns to its original position after being stretched or compressed.

## 2. What factors affect the frequency of oscillation in a spring?

The frequency of oscillation in a spring is affected by its stiffness, or spring constant, and the mass of the object attached to the spring. The stiffer the spring and the lower the mass, the higher the frequency of oscillation.

## 3. How does the amplitude of a spring's oscillation change over time?

The amplitude of a spring's oscillation decreases over time due to the effects of friction and air resistance. This is known as damping.

## 4. Can the length of a spring affect its oscillation?

Yes, the length of a spring can affect its oscillation. A longer spring will have a lower frequency of oscillation compared to a shorter spring with the same stiffness and mass.

## 5. What is the equation for calculating the frequency of oscillation in a spring?

The equation for calculating the frequency of oscillation in a spring is f = 1/(2π√(k/m)), where f is frequency, k is the spring constant, and m is the mass attached to the spring.

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