# Finding the period and frequency for simple harmonic motion [closed]

A 1 lb weight is suspended from a spring. Let y give the deflection (in inches) of the weight from its static deflection position, where “up” is the positive direction for y. If the static deflection is 24 in, ﬁnd a differential equation for y. Solve, and determine the period and frequency of the simple harmonic motion (SHM) of the weight if it is set in motion.

I'm having a hard time coming up with a solvable differential equation to the problem. I'm fairly certain that the motion can be modeled with $my'' + ky = 0$, but I don't really know where that gets me. Any ideas?

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 $my^{\prime\prime} + ky =0$ is your equation of interest. It's a standard 2nd order differential equation and every maths textbook involving differential equations tells you how to solve it. – Sami Kujala Oct 25 '12 at 7:00 So do I use $m = 1$ and $k = ?$. I know how to solve the second order equation, but I'm unsure what the conditions are. Is my initial condition $y(0) = 24$? – Bob John Oct 25 '12 at 7:02 you should get value for $k$ from the given information of static deflection, I think. – Sami Kujala Oct 25 '12 at 7:04 Any idea on how I can do that? What will the units be for k? – Bob John Oct 25 '12 at 7:06 The problem setting already has all the necessary information. A 1 lb weight causes 24 in static deflection, which means that then the weight is in balance, which means...? $k$ will in units of 1/length. – Sami Kujala Oct 25 '12 at 7:11