What is the oscillation frequency?

[lijoeman]

What is mass and speed of the ball?

A spring with spring constant 17 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 7.5 cm and released. The ball makes 16 oscillations in 22 s seconds.

1) What is its the mass of the ball? (in g)
2) What is its maximum speed? (in cm/s)

 

[tiny-tim]

Welcome to PF!

Hi lijoeman! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[nlightner]

The oscillation frequency refers to the number of complete oscillations or back-and-forth movements a system undergoes in a given time period. In this case, the oscillation frequency would be 16 oscillations in 22 seconds, or approximately 0.73 oscillations per second.

In order to determine the mass and speed of the ball, we can use the equation for the period of a simple harmonic motion system: T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. Rearranging this equation, we can solve for the mass of the ball: m = (T/2π)^2 * k. Plugging in the given values, we get m = (22/2π)^2 * 17 = 0.97 g.

To calculate the maximum speed of the ball, we can use the equation v = ωA, where v is the maximum speed, ω is the angular frequency (2π/T), and A is the amplitude (7.5 cm in this case). So, v = (2π/22) * 7.5 = 0.86 cm/s. This would be the maximum speed of the ball as it oscillates between its highest and lowest points.