# Oscillation, Frequency, Amplitude etc Hmwk Problem

1. Jan 25, 2010

### LBRRIT2390

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

A 200g mass attached to a horrizontal spring oscillates at a frequency of 2.0 Hz. At one instant, the mass is at x=5.0cm and has vx = -30cm/s.

A. Determine the period. T= ____seconds

B. Determine the amplitude. A =____cm

C. Determine the maximum speed. vmax = ____ cm/s

D. Determine the total energy. ____ J

2. Relevant equations

A. T = 1/frequency

B. ????

C. vmax= 2(pi)(f)(A) = 2piA/T

D. ????

Others: deltaL = mg/k where k=spring constant

3. The attempt at a solution

A. Answer = 0.5 seconds from T = 1/f.... T = 1/(2.0Hz).... T=0.5 secods

B.

C. vmax=2pi(2.0Hz)(A)

D.

I'm not looking for just the answers; I am in desperate need of an explanation of HOW to do the problem. Any help is greatly appreciated!!!

2. Jan 26, 2010

### kuruman

Mechanical energy is conserved. What is the mechanical energy when the mass is at x=5.0 cm and has vx = -30 cm/s? That's the answer to part D.

What is an expression for the mechanical energy when the particle is at maximum displacement, i.e. when x = A? Write an equation and solve for A. This will give you the answer to part B.

3. Jan 26, 2010

### LBRRIT2390

Thank you,
I was able out to figure out the problem last night by following a post on yahoo. I want to post it step by step here for other stumped students:

Part B. Determine the amplitude.
w = 2(pi)f
w = 2(pi)(2.0Hz)

v = w Sqrt(A2-x2)
-0.30 = (12.6rad/sec) Sqrt[ (A2) - (0.502m) ]
-0.0238 = Sqrt[ (A2) - 0.25 ]
-0.02382 = A2 - 0.25
-5.6644x10-4 = A2 - 0.25
0.2494 = A2
Sqrt (0.2494) = A
A = 0.4994m --> 5.0 cm
****** However, the correct answer from Mastering Physics is 5.5cm, where did I mess up?
A = 5.5 cm

Part C. Determine the maximum speed.
vmax = wA
vmax = 0.69m --> 70 cm

Part D. Determine the total energy.
Etotal = (mvmax2) / 2
Etotal = (0.2kg)(0.72m) / 2
Etotal = 0.049 J

4. Jan 26, 2010

### kuruman

When you square both sides, the left side must be positive.

5. Jan 26, 2010

### LBRRIT2390

Oh! thank you so much kuruman!!!