A 1.90-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 14.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations.

Where does this maximum speed occur?

I don't know what formula to use.

Do you go to ryerson engineering aswell? I'm stuck on this question too. :(

To determine where the maximum speed occurs in a simple harmonic motion system, you can use the concept of energy conservation.

The formula to find the maximum speed in simple harmonic motion is:

v_max = Aω

where v_max is the maximum speed, A is the amplitude of oscillation, and ω (omega) is the angular frequency.

To find the amplitude (A), you can use the displacement given in the problem statement. The object is pulled 0.200 m from the equilibrium position, so the amplitude will be half of that: A = 0.200 m / 2 = 0.100 m.

To find the angular frequency (ω), you can use the relationship between angular frequency, mass (m), and spring constant (k):

ω = √(k/m)

However, we don't have the spring constant or the angular frequency explicitly given in the problem statement.

To find the spring constant (k), we need to use Hooke's Law:

F = -kx

where F is the force applied, k is the spring constant, and x is the displacement from equilibrium.

In the problem statement, it says a force of 14.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position. Since the force is directed opposite to the displacement, we have:

14.0 N = -k(0.200 m)

Solving for k, we find:

k = -14.0 N / (0.200 m)

Now that we have the spring constant (k) and the mass (m) given (1.90 kg), we can find the angular frequency:

ω = √(k/m)

To find the maximum speed (v_max), we substitute the values of A and ω into the equation:

v_max = Aω

v_max = (0.100 m) x √(k/m)

Now you have all the information you need to find the maximum speed (v_max) by substituting the values of A, k, and m into the equation.