Question

We are still looking at the oscillating thingy hanging from a spring. The system was set vibrating by pulling the thingy down below its equilibrium position and then letting it go from rest. If the initial displacement is doubled what happens to the maximum kinetic energy of the thing?

• A. It is unchanged.
• B. It is doubled.
• C. It is increased by a factor of 4.
• D. We can't tell from the information provided.

Answer 1

The correct option is C It is increased by a factor of 4.

Maximum kinetic energy (KE) occurs when the thingy's speed is greatest and is proportional to the square of that speed. The maximum speed occurring at the equilibrium point is given by $A\omega$, A being the amplitude and $\omega$ being the angular frequency. Since, $\omega$ is irrespective of displacement so, velocity depends on the amplitude and doubling A results in increasing maximum kinetic energy by a factor of 4.