Find maximum speed of mass on spring

[yosimba2000]

Homework Statement

Find the maximum speed of the mass on a spring.

The spring and mass are lying on a horizontal surface, with the spring being attached to both the wall and mass. The mass is 8kg and the spring constant is 784 N/m. The spring, at resting state, is 20cm (0.2m), but the spring is currently stretched to 25cm (.25m).

f (frequency) is 1.576 Hz (this I calculated, it was not given so it could be wrong.).

Homework Equations

I found this EQ online for Vmax: fA = 2pi

f = frequency
A = amplitude

The Attempt at a Solution

I was think of using the above formula, but I don't know how to find the Amplitude.

I have taken AP Calculus AB, but the Physics course I am taking is non- calculus based, so please try not to explain in calculus terms.

I do know that the mass has the maximum velocity right when it passes the equilibrium point.

Thanks!

*wait, i just saw you can solve for A from the fA=2pi. But how does this formula work for a spring if I have all the variables for the formula?

 

[Delphi51]

Do you have formulas for the motion of the mass like this:
http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html#c1
There is a similar one for the velocity, which you could obtain by differentiating that one.

Or you could take an energy approach. The mass initially has spring energy. That is entirely converted into kinetic energy at the point where the speed is greatest. If you have formulas for spring and kinetic energy, that's probably the easiest approach.

 

[yosimba2000]

to use the kinetic and spring energy approach, how would I do that?

I know that kinetic energy (Fk) is .5m(v^2).

Is Spring energy .5k(x^2)?

 

[Delphi51]

Initial spring energy = maximum kinetic energy

 

[asteriatic]

I would like to clarify that the maximum speed of the mass on a spring is dependent on the amplitude of the oscillation, as well as the mass and spring constant. The formula fA = 2pi is not applicable in this situation as it is used for simple harmonic motion in a pendulum, not a spring.

To find the maximum speed of the mass on a spring, we can use the equation for the period of oscillation: T = 2pi * sqrt(m/k), where T is the period, m is the mass, and k is the spring constant. From this equation, we can solve for the amplitude, A, by rearranging to A = T^2 * k / (4pi^2 * m).

In this case, the amplitude can be calculated as A = (1/1.576)^2 * 784 / (4 * 3.14^2 * 8) = 0.063 m.

Using the amplitude, we can then calculate the maximum speed of the mass as v = 2pi * f * A = 2 * 3.14 * 1.576 * 0.063 = 0.397 m/s.

It is important to note that this is the maximum speed at the equilibrium point, when the spring is neither stretched nor compressed. The speed at any other point in the oscillation will be lower. Additionally, if the initial conditions (initial displacement and velocity) of the mass on the spring are not given, we cannot accurately determine the maximum speed.