An object of unknown mass $m$ is hung from a vertical spring of unknown spring constant $k$, and the object is observed to be at rest when the spring has stretched by 14 cm. The object is then given a slight push upward and executes SHM. Determine the period $T$ of this oscillation.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Period is 2π times the square root of mass divided by the spring constant, neither of which we know. But we do know that when the mass is initially hung from the spring and it's at rest here, it's stretching the spring by this distance x and it's stationary there. And so the spring force upwards which equals kx is going to equal the gravity down mg. And so we can divide both sides by kg and we get that m over k equals x over g. And so we can make that substitution now into our period formula. So, period is 2π times square root of x over g instead of m over k. And that's 2π times the square root of 14 times 10 to the minus 2 meters divided by 9.8 meters per second squared and that gives 0.75 seconds for the period.