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A spring with force constant k is attached at one end to a wall and at the other end to a block of mass m resting on a smooth horizontal surface. Another wall is located at a distance x0 from the block (at the spring's natural length position). The spring is compressed by 2*x0 and then released. How long does it take the block to reach and strike the second wall?

1. (1/6)*pi*sqrt(m/k)
2. sqrt(m/k)
3. (2*pi/3)*sqrt(m/k)
4. (pi/4)*sqrt(m/k)

Correct answer: (2*pi/3)*sqrt(m/k)

Solution

In SHM starting at maximum compression 2x0, the block reaches the wall position (at x0 away from equilibrium) when cos(omega*t) = -1/2, giving t = (2*pi/3)*sqrt(m/k).

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