# Homework Help: Oscillatory Motion and Periods

1. Jan 26, 2012

### kgal

1. The problem statement, all variables and given/known data
A student measures the unstretched length of a spring as 11.2 cm. When a 100.0 g mass is hung from the end of the spring, its length is 20.7 at rest. The mass-spring system is set into oscillatory motion and the amplitude of the motion decreases to half its original value in 5 complete oscillations.
a. What is the period of the oscillatory motion, assuming no damping?
b. The student can measure the period of oscillation to an accuracy of 0.05s. Will the student be able to detect the difference between the period calculated with no damping and the period of the damped oscillator?

2. Relevant equations

F = -kΔx
T = 2∏/√(k/m)
Δx = x2 - x1

3. The attempt at a solution

a. Δx = x2 - x1 = 20.7 - 11.2 = 9.5 cm = 0.095 m
F = -kΔx
-k = F/Δx = mg/Δx = .98/.095 = 10.31 N/m
T = 2∏ / √(k/m) = .62 s

b. Not sure how to even start with this one....
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 27, 2012

### Spinnor

#### Attached Files:

• ###### damped h.o..png
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3. Jan 28, 2012

### kgal

is the original amplitude the difference between the spring natural length and the spring length after the mass is put on it?

4. Jan 28, 2012

### Spinnor

No, the amplitude is not given and not needed for the problem. Just assume it is some value and what is important is what ever the value is it halves as stated in the problem.

5. Feb 22, 2012

### kampfer

What about part b?
Did you find difference between the period calculated with no damping and the period of the damped oscillator?

Last edited: Feb 22, 2012