Tessellate S.T.E.M.S (2019) - Physics - Category C - Set 1 - Objective Problem 1

Level 2

Let $E$ be the energy of the particle.

Where the potential $V$ is given by:

$V = \cases{ \frac{1}{2}kx^2 \quad \text{if } x< 0 \\ mgx \quad \text{if } x >0 }$

What is the time period of oscillation?

\pi \sqrt{\frac{m}{k}} + 2\sqrt{\frac{2E}{mg^2}}

2\pi \sqrt{\frac{m}{k}}

2 \sqrt{2E/mg^2}

2\pi\sqrt{\frac{m}{k}} + 4\sqrt{\frac{2E}{mg^2}}

\sqrt{\frac{k}{m}}

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