- #1
superdave
- 150
- 3
Homework Statement
1. A particle of mass m is constrained to move along a straight line. In a certain
region of motion near x = 0 , the force acting on the particle is F = -F_0 sin(bx) , where F_0 and b are positive constants.
(a) Find the potential energy of the particle in this region. Sketch this potential; label the axes.
(b) If at time t = 0 the particle was at x = 0 and had velocity v_0 , find the turning points of theparticle’s motion.
(c) Find the period of the particle’s small harmonic oscillations about the equilibrium point.
What condition must be satisfied for the oscillations to be “small”?
Homework Equations
F = - dV/dx
The Attempt at a Solution
Part a)
So I get V = -int(F) = - F_0/b cos (bx). But I'm confused about the usual + C you get when doing an integral. I guess that would be V_0 which would be - F_0/b cos (b * x_0)? So does V = -F_0/b cos (bx) - F_0/b cos (bx_0)? And in that case, wouldn't it be pretty impossible to sketch without knowing x_0 which isn't defined in this part of the problem?
part b)
Umm, okay. so I get a=-a_0 sin(bx) = dv/dt. v = integral (a dt) = -a_0 * t * sin(bx) + v_0
So this confuses me, so I guess turning points are when t*sin(bx) = v_0/a_0? That's kind of a random answer and doesn't sit well.
part c)
I have no idea