Determine the period and frequency of SHM

[zaboda42]

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 your equation and determine the period and frequency of the simple harmonic motion of the weight if it is set in motion.

I'm having a hard time starting, I don't know how to set up the differential equation. I assume that an initial position will be y(24) = 1, but I can't get past the initial assumptions.

Anything to help?

Thanks!

 

[haruspex]

I think you mean y(0)=24.
What are the forces on the weight when the deflection is y? What acceleration will result? How do you express the acceleration in terms of y and t?

 

[zaboda42]

I know that a potential differential equation may be my'' + ky = 0. Does this get me anywhere?

 

[zaboda42]

Any thoughts?

 

[haruspex]

Let the modulus of the spring be k. When the deflection is y, what is the upward force exerted by the spring? (Be careful with signs.) What other forces act on the weight? What is the net force? How does that relate to the acceleration of y?