Horizontal Spring Displacement

The displacement of a mass from its equilibrium position as it oscillates on a horizontal spring satisfies the equation \(x(t) = A\cos(\omega t + \phi_0)\).

Part 1(a)

At \(t = 0\) s, if \(x = -A/{{ params.n}}\), There are the two possible values of \(\phi_0\) between 0 and 2\(\pi\) radians.

Enter the smaller angle;

Answer Section

Please enter an integer value in .

Part 1(b)

Enter the larger angle;

Answer Section

Please enter an integer value in .

Part 2

At \(t = 0\) s, what fraction of the total energy of this oscillator is spring potential energy?

Answer Section

Please enter an integer value in .

Part 3(a)

At \(t = 0\) s, there are two possible values of the \(x\)-components of the velocity of the mass (\(v_x\)) in terms of \(v\_{max}\) that are found when \(x = -A/{{ params.n}}\).

Which value of \(\phi_0\) belongs to the larger angle?

Answer Section

Please enter an integer value in .

Part 3(b)

Which value of \(\phi_0\) belongs to the smaller angle?

Answer Section

Please enter an integer value in .

Part 4

Choosing the value of \(\phi_0\) from part (a) between 0 and \(\pi\), at what times between 0 and \(T\) are the kinetic and potential energies equal?

Answer Section

Please enter an integer value in .

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.