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Grade: 11

                        

calculate the time period of the oscillation of a particle of mass m moving in the potential defined as U(x)=1/2kx2,x0

2 years ago

Answers : (1)

Susmita
425 Points
							
U=kx2/2
force F=-dU/dx=-kx
Force equation
md2x/dt2=-kx
or,md2x/dt2+kx=0
Or,d2x/dt2+(k/m)x=0
or,d2x/dt2+w2x=0
where we let w2=k/m for convenience.
Let us take x=sinbt as a trial solution.
dx/dt=bcosbt
d2x/dt2=-b2sinbt=-b2x
or,d2x/dt2+b2x=0
So sinbt satisfies the equation and comparing
b2=w2
or,b=w.
So x=sinwt
Frequency=f=w/2pi
Time period T=1/f=2pi/w=2pi×root(m/k)
 
2 years ago
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