# 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 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

## Homework Equations

A. T = 1/frequency

B. ?

C. vmax= 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. 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!

Homework Helper
Gold Member
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)

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

Homework Helper
Gold Member
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!