- #1
NATURE.M
- 301
- 0
Homework Statement
A cube of mass m is connected to two rubber bands of length L, each under tension T. The cube is displaced by a small distance y perpendicular to the length of the rubber bands. Assume the tension doesn't change. Show that the system exhibits SHM, and find its angular freqency ω.
The Attempt at a Solution
So basically from a FBD of cube, I have vertical forces: -2Tsinθ - mg = m[itex]\frac{d^2y}{dt^2}[/itex] and the horizontal components of tension from each band cancels. Now since the cube is displaced by a small distance y, I assume we can approximate sinθ ≈ θ. But then I'm not sure what to do?
I tried using sinθ = [itex]\frac{y}{(y^2+L^2)^{1/2}}[/itex], but then I get a complicated expression.
I know I need to obtain a -constant*y on the LHS. Any suggestions.