Oscillation, Frequency, Amplitude etc Hmwk Problem

[LBRRIT2390]

Homework Statement

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 v_x = -30cm/s.

A. Determine the period. T= ____seconds

B. Determine the amplitude. A =____cm

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

D. Determine the total energy. ____ J

Homework Equations

A. T = 1/frequency

B. ?

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

D. ?

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

The Attempt at a Solution

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

B.

C. v_max=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!

 

[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.

 

[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)
w = 12.6 rad/sec

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.
v_max = wA
v_max = (12.6rad/s)(0.055m)
v_max = 0.69m --> 70 cm

Part D. Determine the total energy.
E_total = (mv_max²) / 2
E_total = (0.2kg)(0.7²m) / 2
E_total = 0.049 J

 

[kuruman]

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?

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

 

[LBRRIT2390]

Oh! thank you so much kuruman!