I've got as far as T=2Pi/w => 1/w=(m/k)^1/2 => w^2=k/m I don't even know what k/m is. I've tried integrating trig graphs, rearranging spring constant equations, all to no avail. If anyone could give me a pointer that would be much appreciated.
I've got as far as T=2Pi/w => 1/w=(m/k)^1/2 => w^2=k/m I don't even know what k/m is. I've tried integrating trig graphs, rearranging spring constant equations, all to no avail. If anyone could give me a pointer that would be much appreciated.
The defining feature of SHM is that a∝−x where x is the displacement from the origin. We usually write the associated equation in the form a=−ω2x, because then after solving, we find that the period is given by T=ω2π.
For a mass on a spring, the restoing force is given by F=ma=−kx where k is the spring constant.
Can you finish it from here? (Hint: rearrange and equate coefficients)
Ah right: ma=−kx[br]a=m−kx[br]a=−ω2x[br]m−kx=−ω2x=>mx−kx=−ω2=>w=mk sub ω back in: [br]T=mk2π=2πkm[br] I didn't think to use the acceleration equation for SHM. Thanks for the help!
This is not correct. You get the correct answer, but you start from an incorrect equation. If you look at your F=maL equation, the units of this equation are incorrect. On the left hand side you have Netwons, and on the right hand side you have Newtons*meters. The correct way to solve this is to start with F=mgtheta, then use the arc length formula to note that theta=arclength/l. Solving for a you get a=g*arclength/l. Then using circular motion, you set a=omega*arclength. Setting the a=a you solve for omega and get omega=sqrt(g/l)