# Homework Help: Finding amplitude of a baby in cot

1. May 19, 2012

### charmedbeauty

1. The problem statement, all variables and given/known data

A baby bounces up and down in her crib. Her mass is 10.5 kg, and the crib mattress can be modeled as a light spring with force constant 654 N/m.

The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency?

b)If she were to use the mattress as a trampoline—losing contact with it for part of each cycle—what minimum amplitude of oscillation does she require?

2. Relevant equations

3. The attempt at a solution

for the first part I just did

T=2∏√(m/k)

and f=1/T

f= 1.256

for part b)

ω=2∏/T

T=1/f

ω=2∏(1.256)

=7.89

is this method correct for b)

2. May 19, 2012

### BruceW

Your method for part a) looks correct. But for part b) you have calculated the natural angular frequency of the system, but the question hasn't asked you to do this. part b) is a slightly odd question. It asks for the required amplitude of oscillation such that the baby leaves the mattress. I don't think there is enough information to find the answer to part b), was there anything else given in the question?

Edit: Oh, I think for part b) you are just supposed to give a word answer. It is a common sense answer, really. You need to think about the situation, no calculation is needed.

3. May 19, 2012

### charmedbeauty

No its definitely a calculation it has a cm units marked next to it.

4. May 20, 2012

### magin

For part b), Is this actually pretty easy? Can you just find the spring displacement that would result in an initial acceleration of -9.8m/s^2 if freely released? So the baby would be accelerating downwards at a lesser rate than the cot spring... leaving the spring?

5. May 20, 2012

### charmedbeauty

you mean find the spring force necessary to overcome the weight force?

6. May 20, 2012

### magin

Yes, would this be correct?

7. May 20, 2012

### charmedbeauty

no

8. May 20, 2012

### magin

and at a displacement of about 16cm... the spring force and baby are in equilibrium

9. May 20, 2012

### magin

I don't think I am wording myself clearly.

If the baby and the mattress were attached to each other, and you pulled the baby upwards by 16 cm and then released it, then the spring force on the baby would result in a downwards acceleration greater than g. The baby and the spring aren't attached however, so it would leave the spring. I think it is fair to think of it like this, at the peak of each oscillation, the baby and spring are momentarily stationary...

10. May 22, 2012

### charmedbeauty

maybe try

A=(gm)/k

that should be right