How Do You Calculate the Amplitude of Oscillation for a Spring-Mass System?

[kristibella]

Homework Statement

A 200 g ball attached to a spring with spring constant
2.50 N/m oscillates horizontally on a frictionless table. Its velocity is 18.0 cm/s when x = -5.00 cm.
A. What is the amplitude of oscillation?

B. What is the speed of the ball when x = 3.00 cm?

Homework Equations

A. $$\omega$$ = sqrt k/m = sqrt 2.50/.200
v(t) = A*$$\omega$$*sin($$\omega$$t)
t = 0
v(t) = A$$\omega$$

B. V_x² = $$\omega$$²(A² - x²)

The Attempt at a Solution

I've tried several times to get a solution and I have never gotten the same answer twice...
A. $$\omega$$ = 3.54
A = 5.09 cm

B. When x = 3.00 cm, V = 14. 56 cm.

Neither of these answers are correct and I'm not sure what I am doing wrong. I am doing everything as explained to me in class. I'm so confused...

 

[Redbelly98]

Have you been taught about conservation of energy, and the potential energy of a spring?

Also, is there supposed to be a question in part A? I only see a question in B.

 

[thomate1]

The amplitude of oscillation is the maximum displacement of the object from its equilibrium position. In this case, the ball is attached to a spring with a spring constant of 2.50 N/m and a mass of 200 g. We can use the equation \omega = sqrt(k/m) to calculate the angular frequency of the oscillation, which is equal to 3.54 rad/s.

To find the amplitude, we can use the equation v(t) = A*\omega*sin(\omegat), where v(t) is the velocity at time t, A is the amplitude, and \omega is the angular frequency. Since the velocity is given as 18.0 cm/s at x = -5.00 cm, we can substitute these values into the equation and solve for A.

18.0 cm/s = A*3.54 rad/s*sin(0)
A = 5.09 cm

Therefore, the amplitude of oscillation is 5.09 cm.

For part B, we can use the equation Vx2 = \omega2(A2 - x2) to find the velocity at x = 3.00 cm. We already know the value of \omega, so we can substitute it into the equation along with the amplitude we calculated in part A.

Vx2 = (3.54 rad/s)2(5.09 cm2 - (3.00 cm)2)
Vx = 14.00 cm/s

Therefore, the speed of the ball when x = 3.00 cm is 14.00 cm/s. It is important to remember to use consistent units throughout the calculations. In this case, we converted the given velocity from cm/s to rad/s in order to use the equation.