A spring oscillator has \(k=120\,\mathrm{N\,m^{-1}}\) and amplitude \(0.050\,\mathrm{m}\). Find its total energy.

Where is the speed of an undamped spring oscillator maximum: at equilibrium or at a turning point?

If the amplitude of an undamped spring oscillator is doubled, by what factor does its total energy change?

An oscillator has total energy \(0.80\,\mathrm{J}\) and spring constant \(100\,\mathrm{N\,m^{-1}}\). Find its amplitude.

At \(x=0\) in an undamped spring oscillator, what are the spring potential energy and kinetic energy in terms of total energy \(E\)?

A \(0.25\,\mathrm{kg}\) mass on a spring has \(k=64\,\mathrm{N\,m^{-1}}\) and amplitude \(0.15\,\mathrm{m}\). Find its maximum speed.

A spring oscillator has amplitude \(A\). What fraction of its total energy is potential energy at \(x=A/2\)?

A spring oscillator has total energy \(2.5\,\mathrm{J}\) and amplitude \(0.25\,\mathrm{m}\). Find the spring constant.

An oscillator has \(E=3.6\,\mathrm{J}\) and mass \(0.80\,\mathrm{kg}\). Find its maximum speed.

A spring oscillator has \(A=0.20\,\mathrm{m}\) and \(\omega=10\,\mathrm{rad\,s^{-1}}\). Find the speed magnitude at \(x=0.12\,\mathrm{m}\).

At \(x=A/3\), what fraction of an undamped spring oscillator's total energy is kinetic energy?

A \(0.50\,\mathrm{kg}\) mass on a spring has speed \(1.2\,\mathrm{m\,s^{-1}}\) as it passes \(x=0.030\,\mathrm{m}\). The spring constant is \(200\,\mathrm{N\,m^{-1}}\). Find the amplitude.

At what displacement magnitude is the kinetic energy equal to the spring potential energy in an undamped oscillator of amplitude \(A\)?

An oscillator has maximum speed \(0.90\,\mathrm{m\,s^{-1}}\) and angular frequency \(6.0\,\mathrm{rad\,s^{-1}}\). Find its amplitude.

At what displacement magnitude is the speed \(80\%\) of its maximum value in an undamped oscillator of amplitude \(A\)?

An oscillator has amplitude \(A\). Derive the displacement magnitude where the speed is half its maximum speed.

A damp-free oscillator loses \(36\%\) of its mechanical energy in a brief interaction and then continues oscillating with the same spring constant. By what factor does its amplitude change?

A mass \(m\) on a spring \(k\) is released from rest at \(x=A\). When it reaches \(x=A/3\), a rough patch removes energy \(Q\) instantly without changing position. Derive the condition on \(Q\) for the mass still to pass through equilibrium, and find its speed there if it does.

A mass \(m\) on a spring \(k\) passes \(x=x_0\) with speed \(v_0\). Derive the amplitude using energy, and state the condition on \(x_0\) and \(v_0\) for the state to be physically possible.

A spring oscillator has amplitude \(A\). A sensor may be active only where the kinetic energy is at least a fraction \(q\) of the total energy. Derive the allowed interval of \(x\), and state the allowed range of \(q\).